Check whether there is a guaranteed amount of water the farmers, ranchers, and cities will get from the Yellowstone River each year.

Question

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Answer 1

Question

Chapter 3, Problem 9CRP

a.

To determine

Check whether there is a guaranteed amount of water the farmers, ranchers, and cities will get from the Yellowstone River each year.

a.

Expert Solution

Answer to Problem 9CRP

No, there is no guaranteed amount of water the farmers, ranchers, and cities get from the Yellowstone River each year.

Explanation of Solution

The important source of water for wildlife, rancher, farmers, and cities downstream is Yellowstone River. The data show that the annual flow for recent 19 years of the Yellowstone River, which does not show any guarantee that they give water for each year.

The annual flows are random variables. Hence, there is no guaranteed amount of water the farmers, ranchers, and cities will get from the Yellowstone River each year.

b.

To determine

Find the expected annual flow from the Yellowstone snowmelt.

Find the mean, median, and mode.

b.

Expert Solution

Answer to Problem 9CRP

The expected annual flow from the Yellowstone snowmelt is 27.05.

The value of mean is 27.05.

The value of median is 25.9.

The value of mode is 25.9.

Explanation of Solution

Step-by-step procedure to obtain the mean, median, and mode using the MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Annual flow.
Check Options, Select Mean, Median and Mode.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 1

From the MINITAB output, the value of mean is 27.05, the value of median is 25.9, and the value of mode is 25.9.

c.

To determine

Find the range and standard deviation of annual flow.

c.

Expert Solution

Answer to Problem 9CRP

The range is 27.6.

The value of standard deviation is 6.61.

Explanation of Solution

Step-by-step procedure to obtain the range and standard deviation using the MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Annual flow.
Check Options, Select Mean, Median and Mode.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 2

From the MINITAB output, the range is 27.6 and the value of standard deviation is 6.61.

d.

To determine

Find the 75% Chebyshev interval around the mean.

d.

Expert Solution

Answer to Problem 9CRP

The 75% Chebyshev interval around the mean is 13.83 and 40.27.

Explanation of Solution

The 75% Chebyshev interval around the mean is obtained below:

x¯−2s=27.05−2(6.61)=27.05−13.22=13.83x¯+2s=27.05+2(6.61)=27.05+13.22=40.27

Thus, the 75% Chebyshev interval around the mean for Grid E is 0.77 and 39.93.

e.

To determine

Find the five-number summary of the annual water flow.

Draw the box-and-whisker plot.

Interpret the five-number summary and box-and-whisker plot.

Find the values where the middle portion of the data lies.

Find the interquartile range.

Identify the data outliers.

e.

Expert Solution

Answer to Problem 9CRP

The five-number summary of the annual water flow is 17.5, 23.7, 25.9, 31.8, and 45.1.

The box-and-whisker plot is shown below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 3

The middle portion of the data lies between 23.7 and 31.8.

The value of interquartile range is 8.1.

The value 45.1 is an outlier.

Explanation of Solution

Step-by-step procedure to obtain the five-number summary of the annual water flow using MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Annual flow.
Check Options, Select Minimum, Maximum, first quartile, Median, third quartile and IQR.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 4

From the MINITAB output, the five-number summary of annual water flow is 17.5, 23.7, 25.9, 31.8, and 45.1.

Step-by-step procedure to draw the box-and-whisker plot using the MINITAB software:

Choose Graph > Boxplot or Stat > EDA > Boxplot.
Under One Y, choose Simple. Click OK.
In Graph variables, enter the data of Annual flow.
Click OK in all dialogue boxes.

Interpretation:

From the box-and-whisker plot, it is observed that the distribution of the annual water flow is skewed to the right.

From the output, it is observed that the middle portion of the data lies between 23.7 and 31.8.

From the MINITAB output, the value of interquartile range is 8.1.

From the box-and-whisker plot, it is observed that the value 45.1 is an outlier.

f.

To determine

Check whether the Madison is more reliable using the coefficient of variation.

f.

Expert Solution

Explanation of Solution

Step-by-step procedure to obtain the coefficient of variation using the MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Yellowstone and Madison.
Check Options, Select coefficient of variation.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 5

From the MINITAB output, the coefficient of variation for the annual water flow of Yellowstone is 24.43, and the coefficient of variation for the annual water flow of Madison is 16.6.

From the result, it is observed that the coefficient of variation for the water flow of Madison is smaller when compared to the coefficient of variation for the annual water flow of Yellowstone. This indicates that the spread of river flow is smaller for Madison river. Hence, the Madison flower is more consistent.

g.

To determine

Check whether it is safe to allocate at least 27 units of Yellowstone River water each year for agricultural and domestic use.

g.

Expert Solution

Explanation of Solution

From the results, it is observed that the median water flow of Yellowstone River is 25.9, which indicates that more than half of the river flows are below 27 units.

Hence, it is not safe to allocate at least 27 units of Yellowstone River water each year for agricultural and domestic use.

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Answer 2

Question

Chapter 3, Problem 9CRP

a.

To determine

Check whether there is a guaranteed amount of water the farmers, ranchers, and cities will get from the Yellowstone River each year.

a.

Expert Solution

Answer to Problem 9CRP

No, there is no guaranteed amount of water the farmers, ranchers, and cities get from the Yellowstone River each year.

Explanation of Solution

The important source of water for wildlife, rancher, farmers, and cities downstream is Yellowstone River. The data show that the annual flow for recent 19 years of the Yellowstone River, which does not show any guarantee that they give water for each year.

The annual flows are random variables. Hence, there is no guaranteed amount of water the farmers, ranchers, and cities will get from the Yellowstone River each year.

b.

To determine

Find the expected annual flow from the Yellowstone snowmelt.

Find the mean, median, and mode.

b.

Expert Solution

Answer to Problem 9CRP

The expected annual flow from the Yellowstone snowmelt is 27.05.

The value of mean is 27.05.

The value of median is 25.9.

The value of mode is 25.9.

Explanation of Solution

Step-by-step procedure to obtain the mean, median, and mode using the MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Annual flow.
Check Options, Select Mean, Median and Mode.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 1

From the MINITAB output, the value of mean is 27.05, the value of median is 25.9, and the value of mode is 25.9.

c.

To determine

Find the range and standard deviation of annual flow.

c.

Expert Solution

Answer to Problem 9CRP

The range is 27.6.

The value of standard deviation is 6.61.

Explanation of Solution

Step-by-step procedure to obtain the range and standard deviation using the MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Annual flow.
Check Options, Select Mean, Median and Mode.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 2

From the MINITAB output, the range is 27.6 and the value of standard deviation is 6.61.

d.

To determine

Find the 75% Chebyshev interval around the mean.

d.

Expert Solution

Answer to Problem 9CRP

The 75% Chebyshev interval around the mean is 13.83 and 40.27.

Explanation of Solution

The 75% Chebyshev interval around the mean is obtained below:

x¯−2s=27.05−2(6.61)=27.05−13.22=13.83x¯+2s=27.05+2(6.61)=27.05+13.22=40.27

Thus, the 75% Chebyshev interval around the mean for Grid E is 0.77 and 39.93.

e.

To determine

Find the five-number summary of the annual water flow.

Draw the box-and-whisker plot.

Interpret the five-number summary and box-and-whisker plot.

Find the values where the middle portion of the data lies.

Find the interquartile range.

Identify the data outliers.

e.

Expert Solution

Answer to Problem 9CRP

The five-number summary of the annual water flow is 17.5, 23.7, 25.9, 31.8, and 45.1.

The box-and-whisker plot is shown below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 3

The middle portion of the data lies between 23.7 and 31.8.

The value of interquartile range is 8.1.

The value 45.1 is an outlier.

Explanation of Solution

Step-by-step procedure to obtain the five-number summary of the annual water flow using MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Annual flow.
Check Options, Select Minimum, Maximum, first quartile, Median, third quartile and IQR.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 4

From the MINITAB output, the five-number summary of annual water flow is 17.5, 23.7, 25.9, 31.8, and 45.1.

Step-by-step procedure to draw the box-and-whisker plot using the MINITAB software:

Choose Graph > Boxplot or Stat > EDA > Boxplot.
Under One Y, choose Simple. Click OK.
In Graph variables, enter the data of Annual flow.
Click OK in all dialogue boxes.

Interpretation:

From the box-and-whisker plot, it is observed that the distribution of the annual water flow is skewed to the right.

From the output, it is observed that the middle portion of the data lies between 23.7 and 31.8.

From the MINITAB output, the value of interquartile range is 8.1.

From the box-and-whisker plot, it is observed that the value 45.1 is an outlier.

f.

To determine

Check whether the Madison is more reliable using the coefficient of variation.

f.

Expert Solution

Explanation of Solution

Step-by-step procedure to obtain the coefficient of variation using the MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Yellowstone and Madison.
Check Options, Select coefficient of variation.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 5

From the MINITAB output, the coefficient of variation for the annual water flow of Yellowstone is 24.43, and the coefficient of variation for the annual water flow of Madison is 16.6.

From the result, it is observed that the coefficient of variation for the water flow of Madison is smaller when compared to the coefficient of variation for the annual water flow of Yellowstone. This indicates that the spread of river flow is smaller for Madison river. Hence, the Madison flower is more consistent.

g.

To determine

Check whether it is safe to allocate at least 27 units of Yellowstone River water each year for agricultural and domestic use.

g.

Expert Solution

Explanation of Solution

From the results, it is observed that the median water flow of Yellowstone River is 25.9, which indicates that more than half of the river flows are below 27 units.

Hence, it is not safe to allocate at least 27 units of Yellowstone River water each year for agricultural and domestic use.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 3, Problem 9CRP

a.

To determine

Check whether there is a guaranteed amount of water the farmers, ranchers, and cities will get from the Yellowstone River each year.

a.

Expert Solution

Answer to Problem 9CRP

No, there is no guaranteed amount of water the farmers, ranchers, and cities get from the Yellowstone River each year.

Explanation of Solution

The important source of water for wildlife, rancher, farmers, and cities downstream is Yellowstone River. The data show that the annual flow for recent 19 years of the Yellowstone River, which does not show any guarantee that they give water for each year.

The annual flows are random variables. Hence, there is no guaranteed amount of water the farmers, ranchers, and cities will get from the Yellowstone River each year.

b.

To determine

Find the expected annual flow from the Yellowstone snowmelt.

Find the mean, median, and mode.

b.

Expert Solution

Answer to Problem 9CRP

The expected annual flow from the Yellowstone snowmelt is 27.05.

The value of mean is 27.05.

The value of median is 25.9.

The value of mode is 25.9.

Explanation of Solution

Step-by-step procedure to obtain the mean, median, and mode using the MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Annual flow.
Check Options, Select Mean, Median and Mode.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 1

From the MINITAB output, the value of mean is 27.05, the value of median is 25.9, and the value of mode is 25.9.

c.

To determine

Find the range and standard deviation of annual flow.

c.

Expert Solution

Answer to Problem 9CRP

The range is 27.6.

The value of standard deviation is 6.61.

Explanation of Solution

Step-by-step procedure to obtain the range and standard deviation using the MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Annual flow.
Check Options, Select Mean, Median and Mode.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 2

From the MINITAB output, the range is 27.6 and the value of standard deviation is 6.61.

d.

To determine

Find the 75% Chebyshev interval around the mean.

d.

Expert Solution

Answer to Problem 9CRP

The 75% Chebyshev interval around the mean is 13.83 and 40.27.

Explanation of Solution

The 75% Chebyshev interval around the mean is obtained below:

x¯−2s=27.05−2(6.61)=27.05−13.22=13.83x¯+2s=27.05+2(6.61)=27.05+13.22=40.27

Thus, the 75% Chebyshev interval around the mean for Grid E is 0.77 and 39.93.

e.

To determine

Find the five-number summary of the annual water flow.

Draw the box-and-whisker plot.

Interpret the five-number summary and box-and-whisker plot.

Find the values where the middle portion of the data lies.

Find the interquartile range.

Identify the data outliers.

e.

Expert Solution

Answer to Problem 9CRP

The five-number summary of the annual water flow is 17.5, 23.7, 25.9, 31.8, and 45.1.

The box-and-whisker plot is shown below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 3

The middle portion of the data lies between 23.7 and 31.8.

The value of interquartile range is 8.1.

The value 45.1 is an outlier.

Explanation of Solution

Step-by-step procedure to obtain the five-number summary of the annual water flow using MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Annual flow.
Check Options, Select Minimum, Maximum, first quartile, Median, third quartile and IQR.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 4

From the MINITAB output, the five-number summary of annual water flow is 17.5, 23.7, 25.9, 31.8, and 45.1.

Step-by-step procedure to draw the box-and-whisker plot using the MINITAB software:

Choose Graph > Boxplot or Stat > EDA > Boxplot.
Under One Y, choose Simple. Click OK.
In Graph variables, enter the data of Annual flow.
Click OK in all dialogue boxes.

Interpretation:

From the box-and-whisker plot, it is observed that the distribution of the annual water flow is skewed to the right.

From the output, it is observed that the middle portion of the data lies between 23.7 and 31.8.

From the MINITAB output, the value of interquartile range is 8.1.

From the box-and-whisker plot, it is observed that the value 45.1 is an outlier.

f.

To determine

Check whether the Madison is more reliable using the coefficient of variation.

f.

Expert Solution

Explanation of Solution

Step-by-step procedure to obtain the coefficient of variation using the MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Yellowstone and Madison.
Check Options, Select coefficient of variation.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 5

From the MINITAB output, the coefficient of variation for the annual water flow of Yellowstone is 24.43, and the coefficient of variation for the annual water flow of Madison is 16.6.

From the result, it is observed that the coefficient of variation for the water flow of Madison is smaller when compared to the coefficient of variation for the annual water flow of Yellowstone. This indicates that the spread of river flow is smaller for Madison river. Hence, the Madison flower is more consistent.

g.

To determine

Check whether it is safe to allocate at least 27 units of Yellowstone River water each year for agricultural and domestic use.

g.

Expert Solution

Explanation of Solution

From the results, it is observed that the median water flow of Yellowstone River is 25.9, which indicates that more than half of the river flows are below 27 units.

Hence, it is not safe to allocate at least 27 units of Yellowstone River water each year for agricultural and domestic use.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 3, Problem 9CRP

a.

To determine

Check whether there is a guaranteed amount of water the farmers, ranchers, and cities will get from the Yellowstone River each year.

a.

Expert Solution

Answer to Problem 9CRP

No, there is no guaranteed amount of water the farmers, ranchers, and cities get from the Yellowstone River each year.

Explanation of Solution

The important source of water for wildlife, rancher, farmers, and cities downstream is Yellowstone River. The data show that the annual flow for recent 19 years of the Yellowstone River, which does not show any guarantee that they give water for each year.

The annual flows are random variables. Hence, there is no guaranteed amount of water the farmers, ranchers, and cities will get from the Yellowstone River each year.

b.

To determine

Find the expected annual flow from the Yellowstone snowmelt.

Find the mean, median, and mode.

b.

Expert Solution

Answer to Problem 9CRP

The expected annual flow from the Yellowstone snowmelt is 27.05.

The value of mean is 27.05.

The value of median is 25.9.

The value of mode is 25.9.

Explanation of Solution

Step-by-step procedure to obtain the mean, median, and mode using the MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Annual flow.
Check Options, Select Mean, Median and Mode.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 1

From the MINITAB output, the value of mean is 27.05, the value of median is 25.9, and the value of mode is 25.9.

c.

To determine

Find the range and standard deviation of annual flow.

c.

Expert Solution

Answer to Problem 9CRP

The range is 27.6.

The value of standard deviation is 6.61.

Explanation of Solution

Step-by-step procedure to obtain the range and standard deviation using the MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Annual flow.
Check Options, Select Mean, Median and Mode.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 2

From the MINITAB output, the range is 27.6 and the value of standard deviation is 6.61.

d.

To determine

Find the 75% Chebyshev interval around the mean.

d.

Expert Solution

Answer to Problem 9CRP

The 75% Chebyshev interval around the mean is 13.83 and 40.27.

Explanation of Solution

The 75% Chebyshev interval around the mean is obtained below:

x¯−2s=27.05−2(6.61)=27.05−13.22=13.83x¯+2s=27.05+2(6.61)=27.05+13.22=40.27

Thus, the 75% Chebyshev interval around the mean for Grid E is 0.77 and 39.93.

e.

To determine

Find the five-number summary of the annual water flow.

Draw the box-and-whisker plot.

Interpret the five-number summary and box-and-whisker plot.

Find the values where the middle portion of the data lies.

Find the interquartile range.

Identify the data outliers.

e.

Expert Solution

Answer to Problem 9CRP

The five-number summary of the annual water flow is 17.5, 23.7, 25.9, 31.8, and 45.1.

The box-and-whisker plot is shown below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 3

The middle portion of the data lies between 23.7 and 31.8.

The value of interquartile range is 8.1.

The value 45.1 is an outlier.

Explanation of Solution

Step-by-step procedure to obtain the five-number summary of the annual water flow using MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Annual flow.
Check Options, Select Minimum, Maximum, first quartile, Median, third quartile and IQR.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 4

From the MINITAB output, the five-number summary of annual water flow is 17.5, 23.7, 25.9, 31.8, and 45.1.

Step-by-step procedure to draw the box-and-whisker plot using the MINITAB software:

Choose Graph > Boxplot or Stat > EDA > Boxplot.
Under One Y, choose Simple. Click OK.
In Graph variables, enter the data of Annual flow.
Click OK in all dialogue boxes.

Interpretation:

From the box-and-whisker plot, it is observed that the distribution of the annual water flow is skewed to the right.

From the output, it is observed that the middle portion of the data lies between 23.7 and 31.8.

From the MINITAB output, the value of interquartile range is 8.1.

From the box-and-whisker plot, it is observed that the value 45.1 is an outlier.

f.

To determine

Check whether the Madison is more reliable using the coefficient of variation.

f.

Expert Solution

Explanation of Solution

Step-by-step procedure to obtain the coefficient of variation using the MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Yellowstone and Madison.
Check Options, Select coefficient of variation.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 5

From the MINITAB output, the coefficient of variation for the annual water flow of Yellowstone is 24.43, and the coefficient of variation for the annual water flow of Madison is 16.6.

From the result, it is observed that the coefficient of variation for the water flow of Madison is smaller when compared to the coefficient of variation for the annual water flow of Yellowstone. This indicates that the spread of river flow is smaller for Madison river. Hence, the Madison flower is more consistent.

g.

To determine

Check whether it is safe to allocate at least 27 units of Yellowstone River water each year for agricultural and domestic use.

g.

Expert Solution

Explanation of Solution

From the results, it is observed that the median water flow of Yellowstone River is 25.9, which indicates that more than half of the river flows are below 27 units.

Hence, it is not safe to allocate at least 27 units of Yellowstone River water each year for agricultural and domestic use.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 3, Problem 9CRP

a.

To determine

Check whether there is a guaranteed amount of water the farmers, ranchers, and cities will get from the Yellowstone River each year.

a.

Expert Solution

Answer to Problem 9CRP

No, there is no guaranteed amount of water the farmers, ranchers, and cities get from the Yellowstone River each year.

Explanation of Solution

The important source of water for wildlife, rancher, farmers, and cities downstream is Yellowstone River. The data show that the annual flow for recent 19 years of the Yellowstone River, which does not show any guarantee that they give water for each year.

The annual flows are random variables. Hence, there is no guaranteed amount of water the farmers, ranchers, and cities will get from the Yellowstone River each year.

b.

To determine

Find the expected annual flow from the Yellowstone snowmelt.

Find the mean, median, and mode.

b.

Expert Solution

Answer to Problem 9CRP

The expected annual flow from the Yellowstone snowmelt is 27.05.

The value of mean is 27.05.

The value of median is 25.9.

The value of mode is 25.9.

Explanation of Solution

Step-by-step procedure to obtain the mean, median, and mode using the MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Annual flow.
Check Options, Select Mean, Median and Mode.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 1

From the MINITAB output, the value of mean is 27.05, the value of median is 25.9, and the value of mode is 25.9.

c.

To determine

Find the range and standard deviation of annual flow.

c.

Expert Solution

Answer to Problem 9CRP

The range is 27.6.

The value of standard deviation is 6.61.

Explanation of Solution

Step-by-step procedure to obtain the range and standard deviation using the MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Annual flow.
Check Options, Select Mean, Median and Mode.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 2

From the MINITAB output, the range is 27.6 and the value of standard deviation is 6.61.

d.

To determine

Find the 75% Chebyshev interval around the mean.

d.

Expert Solution

Answer to Problem 9CRP

The 75% Chebyshev interval around the mean is 13.83 and 40.27.

Explanation of Solution

The 75% Chebyshev interval around the mean is obtained below:

x¯−2s=27.05−2(6.61)=27.05−13.22=13.83x¯+2s=27.05+2(6.61)=27.05+13.22=40.27

Thus, the 75% Chebyshev interval around the mean for Grid E is 0.77 and 39.93.

e.

To determine

Find the five-number summary of the annual water flow.

Draw the box-and-whisker plot.

Interpret the five-number summary and box-and-whisker plot.

Find the values where the middle portion of the data lies.

Find the interquartile range.

Identify the data outliers.

e.

Expert Solution

Answer to Problem 9CRP

The five-number summary of the annual water flow is 17.5, 23.7, 25.9, 31.8, and 45.1.

The box-and-whisker plot is shown below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 3

The middle portion of the data lies between 23.7 and 31.8.

The value of interquartile range is 8.1.

The value 45.1 is an outlier.

Explanation of Solution

Step-by-step procedure to obtain the five-number summary of the annual water flow using MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Annual flow.
Check Options, Select Minimum, Maximum, first quartile, Median, third quartile and IQR.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 4

From the MINITAB output, the five-number summary of annual water flow is 17.5, 23.7, 25.9, 31.8, and 45.1.

Step-by-step procedure to draw the box-and-whisker plot using the MINITAB software:

Choose Graph > Boxplot or Stat > EDA > Boxplot.
Under One Y, choose Simple. Click OK.
In Graph variables, enter the data of Annual flow.
Click OK in all dialogue boxes.

Interpretation:

From the box-and-whisker plot, it is observed that the distribution of the annual water flow is skewed to the right.

From the output, it is observed that the middle portion of the data lies between 23.7 and 31.8.

From the MINITAB output, the value of interquartile range is 8.1.

From the box-and-whisker plot, it is observed that the value 45.1 is an outlier.

f.

To determine

Check whether the Madison is more reliable using the coefficient of variation.

f.

Expert Solution

Explanation of Solution

Step-by-step procedure to obtain the coefficient of variation using the MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Yellowstone and Madison.
Check Options, Select coefficient of variation.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 5

From the MINITAB output, the coefficient of variation for the annual water flow of Yellowstone is 24.43, and the coefficient of variation for the annual water flow of Madison is 16.6.

From the result, it is observed that the coefficient of variation for the water flow of Madison is smaller when compared to the coefficient of variation for the annual water flow of Yellowstone. This indicates that the spread of river flow is smaller for Madison river. Hence, the Madison flower is more consistent.

g.

To determine

Check whether it is safe to allocate at least 27 units of Yellowstone River water each year for agricultural and domestic use.

g.

Expert Solution

Explanation of Solution

From the results, it is observed that the median water flow of Yellowstone River is 25.9, which indicates that more than half of the river flows are below 27 units.

Hence, it is not safe to allocate at least 27 units of Yellowstone River water each year for agricultural and domestic use.

Answer 6

Chapter 3, Problem 9CRP

a.

To determine

Check whether there is a guaranteed amount of water the farmers, ranchers, and cities will get from the Yellowstone River each year.

a.

Expert Solution

Answer to Problem 9CRP

No, there is no guaranteed amount of water the farmers, ranchers, and cities get from the Yellowstone River each year.

Explanation of Solution

The important source of water for wildlife, rancher, farmers, and cities downstream is Yellowstone River. The data show that the annual flow for recent 19 years of the Yellowstone River, which does not show any guarantee that they give water for each year.

The annual flows are random variables. Hence, there is no guaranteed amount of water the farmers, ranchers, and cities will get from the Yellowstone River each year.

Answer 7

Chapter 3, Problem 9CRP

a.

To determine

Check whether there is a guaranteed amount of water the farmers, ranchers, and cities will get from the Yellowstone River each year.

Answer 8

a.

Expert Solution

Answer to Problem 9CRP

No, there is no guaranteed amount of water the farmers, ranchers, and cities get from the Yellowstone River each year.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

The important source of water for wildlife, rancher, farmers, and cities downstream is Yellowstone River. The data show that the annual flow for recent 19 years of the Yellowstone River, which does not show any guarantee that they give water for each year.

The annual flows are random variables. Hence, there is no guaranteed amount of water the farmers, ranchers, and cities will get from the Yellowstone River each year.

Answer 13

b.

To determine

Find the expected annual flow from the Yellowstone snowmelt.

Find the mean, median, and mode.

b.

Expert Solution

Answer to Problem 9CRP

The expected annual flow from the Yellowstone snowmelt is 27.05.

The value of mean is 27.05.

The value of median is 25.9.

The value of mode is 25.9.

Explanation of Solution

Step-by-step procedure to obtain the mean, median, and mode using the MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Annual flow.
Check Options, Select Mean, Median and Mode.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 1

From the MINITAB output, the value of mean is 27.05, the value of median is 25.9, and the value of mode is 25.9.

Answer 14

b.

To determine

Find the expected annual flow from the Yellowstone snowmelt.

Find the mean, median, and mode.

Answer 15

b.

Expert Solution

Answer to Problem 9CRP

The expected annual flow from the Yellowstone snowmelt is 27.05.

The value of mean is 27.05.

The value of median is 25.9.

The value of mode is 25.9.

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Step-by-step procedure to obtain the mean, median, and mode using the MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Annual flow.
Check Options, Select Mean, Median and Mode.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 1

From the MINITAB output, the value of mean is 27.05, the value of median is 25.9, and the value of mode is 25.9.

Answer 20

c.

To determine

Find the range and standard deviation of annual flow.

c.

Expert Solution

Answer to Problem 9CRP

The range is 27.6.

The value of standard deviation is 6.61.

Explanation of Solution

Step-by-step procedure to obtain the range and standard deviation using the MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Annual flow.
Check Options, Select Mean, Median and Mode.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 2

From the MINITAB output, the range is 27.6 and the value of standard deviation is 6.61.

Answer 21

c.

To determine

Find the range and standard deviation of annual flow.

Answer 22

c.

Expert Solution

Answer to Problem 9CRP

The range is 27.6.

The value of standard deviation is 6.61.

Answer 23

c.

Expert Solution

Answer 24

c.

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Step-by-step procedure to obtain the range and standard deviation using the MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Annual flow.
Check Options, Select Mean, Median and Mode.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 2

From the MINITAB output, the range is 27.6 and the value of standard deviation is 6.61.

Answer 27

d.

To determine

Find the 75% Chebyshev interval around the mean.

d.

Expert Solution

Answer to Problem 9CRP

The 75% Chebyshev interval around the mean is 13.83 and 40.27.

Explanation of Solution

The 75% Chebyshev interval around the mean is obtained below:

x¯−2s=27.05−2(6.61)=27.05−13.22=13.83x¯+2s=27.05+2(6.61)=27.05+13.22=40.27

Thus, the 75% Chebyshev interval around the mean for Grid E is 0.77 and 39.93.

Answer 28

d.

To determine

Find the 75% Chebyshev interval around the mean.

Answer 29

d.

Expert Solution

Answer to Problem 9CRP

The 75% Chebyshev interval around the mean is 13.83 and 40.27.

Answer 30

d.

Expert Solution

Answer 31

d.

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

The 75% Chebyshev interval around the mean is obtained below:

x¯−2s=27.05−2(6.61)=27.05−13.22=13.83x¯+2s=27.05+2(6.61)=27.05+13.22=40.27

Thus, the 75% Chebyshev interval around the mean for Grid E is 0.77 and 39.93.

Answer 34

e.

To determine

Find the five-number summary of the annual water flow.

Draw the box-and-whisker plot.

Interpret the five-number summary and box-and-whisker plot.

Find the values where the middle portion of the data lies.

Find the interquartile range.

Identify the data outliers.

e.

Expert Solution

Answer to Problem 9CRP

The five-number summary of the annual water flow is 17.5, 23.7, 25.9, 31.8, and 45.1.

The box-and-whisker plot is shown below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 3

The middle portion of the data lies between 23.7 and 31.8.

The value of interquartile range is 8.1.

The value 45.1 is an outlier.

Explanation of Solution

Step-by-step procedure to obtain the five-number summary of the annual water flow using MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Annual flow.
Check Options, Select Minimum, Maximum, first quartile, Median, third quartile and IQR.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 4

From the MINITAB output, the five-number summary of annual water flow is 17.5, 23.7, 25.9, 31.8, and 45.1.

Step-by-step procedure to draw the box-and-whisker plot using the MINITAB software:

Choose Graph > Boxplot or Stat > EDA > Boxplot.
Under One Y, choose Simple. Click OK.
In Graph variables, enter the data of Annual flow.
Click OK in all dialogue boxes.

Interpretation:

From the box-and-whisker plot, it is observed that the distribution of the annual water flow is skewed to the right.

From the output, it is observed that the middle portion of the data lies between 23.7 and 31.8.

From the MINITAB output, the value of interquartile range is 8.1.

From the box-and-whisker plot, it is observed that the value 45.1 is an outlier.

Answer 35

e.

To determine

Find the five-number summary of the annual water flow.

Draw the box-and-whisker plot.

Interpret the five-number summary and box-and-whisker plot.

Find the values where the middle portion of the data lies.

Find the interquartile range.

Identify the data outliers.

Answer 36

e.

Expert Solution

Answer to Problem 9CRP

The five-number summary of the annual water flow is 17.5, 23.7, 25.9, 31.8, and 45.1.

The box-and-whisker plot is shown below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 3

The middle portion of the data lies between 23.7 and 31.8.

The value of interquartile range is 8.1.

The value 45.1 is an outlier.

Answer 37

e.

Expert Solution

Answer 38

e.

Expert Solution

Answer 39

Expert Solution

Answer 40

Explanation of Solution

Step-by-step procedure to obtain the five-number summary of the annual water flow using MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Annual flow.
Check Options, Select Minimum, Maximum, first quartile, Median, third quartile and IQR.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 4

From the MINITAB output, the five-number summary of annual water flow is 17.5, 23.7, 25.9, 31.8, and 45.1.

Step-by-step procedure to draw the box-and-whisker plot using the MINITAB software:

Choose Graph > Boxplot or Stat > EDA > Boxplot.
Under One Y, choose Simple. Click OK.
In Graph variables, enter the data of Annual flow.
Click OK in all dialogue boxes.

Interpretation:

From the box-and-whisker plot, it is observed that the distribution of the annual water flow is skewed to the right.

From the output, it is observed that the middle portion of the data lies between 23.7 and 31.8.

From the MINITAB output, the value of interquartile range is 8.1.

From the box-and-whisker plot, it is observed that the value 45.1 is an outlier.

Answer 41

f.

To determine

Check whether the Madison is more reliable using the coefficient of variation.

f.

Expert Solution

Explanation of Solution

Step-by-step procedure to obtain the coefficient of variation using the MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Yellowstone and Madison.
Check Options, Select coefficient of variation.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 5

From the MINITAB output, the coefficient of variation for the annual water flow of Yellowstone is 24.43, and the coefficient of variation for the annual water flow of Madison is 16.6.

From the result, it is observed that the coefficient of variation for the water flow of Madison is smaller when compared to the coefficient of variation for the annual water flow of Yellowstone. This indicates that the spread of river flow is smaller for Madison river. Hence, the Madison flower is more consistent.

Answer 42

f.

To determine

Check whether the Madison is more reliable using the coefficient of variation.

Answer 43

f.

Expert Solution

Explanation of Solution

Step-by-step procedure to obtain the coefficient of variation using the MINITAB software:

Choose Stat > Basic Statistics > Display Descriptive Statistics.
In Variables enter the columns Yellowstone and Madison.
Check Options, Select coefficient of variation.
Click OK in all dialogue boxes.

The output obtained using the MINITAB software is given below:

UNDERSTANDABLE STAT. >PRINT UPGRADE<, Chapter 3, Problem 9CRP , additional homework tip 5

From the MINITAB output, the coefficient of variation for the annual water flow of Yellowstone is 24.43, and the coefficient of variation for the annual water flow of Madison is 16.6.

From the result, it is observed that the coefficient of variation for the water flow of Madison is smaller when compared to the coefficient of variation for the annual water flow of Yellowstone. This indicates that the spread of river flow is smaller for Madison river. Hence, the Madison flower is more consistent.

Answer 44

f.

Expert Solution

Answer 45

f.

Expert Solution

Answer 46

Expert Solution

Answer 47

g.

To determine

Check whether it is safe to allocate at least 27 units of Yellowstone River water each year for agricultural and domestic use.

g.

Expert Solution

Explanation of Solution

From the results, it is observed that the median water flow of Yellowstone River is 25.9, which indicates that more than half of the river flows are below 27 units.

Hence, it is not safe to allocate at least 27 units of Yellowstone River water each year for agricultural and domestic use.

Answer 48

g.

To determine

Check whether it is safe to allocate at least 27 units of Yellowstone River water each year for agricultural and domestic use.

Answer 49

g.

Expert Solution

Explanation of Solution

From the results, it is observed that the median water flow of Yellowstone River is 25.9, which indicates that more than half of the river flows are below 27 units.

Hence, it is not safe to allocate at least 27 units of Yellowstone River water each year for agricultural and domestic use.

Answer 50

g.

Expert Solution

Answer 51

g.

Expert Solution

Answer 52

Expert Solution

Answer 53

Ch. 3.1 - Statistical Literacy Consider the mode, median,...Ch. 3.1 - Prob. 2P Ch. 3.1 - Prob. 3P Ch. 3.1 - Prob. 4P Ch. 3.1 - Prob. 5P Ch. 3.1 - Basic Computation: Mean, Median, Mode Find the...Ch. 3.1 - Prob. 7P Ch. 3.1 - Critical Thinking Consider a data set with at...Ch. 3.1 - Critical Thinking Consider a data set with at...Ch. 3.1 - Prob. 10P

Check whether there is a guaranteed amount of water the farmers, ranchers, and cities will get from the Yellowstone River each year.

Videos

Check whether there is a guaranteed amount of water the farmers, ranchers, and cities will get from the Yellowstone River each year.

Answer to Problem 9CRP

Explanation of Solution

Find the expected annual flow from the Yellowstone snowmelt.

Find the mean, median, and mode.

Answer to Problem 9CRP

Explanation of Solution

Find the range and standard deviation of annual flow.

Answer to Problem 9CRP

Explanation of Solution

Find the 75% Chebyshev interval around the mean.

Answer to Problem 9CRP

Explanation of Solution

Find the five-number summary of the annual water flow.

Draw the box-and-whisker plot.

Interpret the five-number summary and box-and-whisker plot.

Find the values where the middle portion of the data lies.

Find the interquartile range.

Identify the data outliers.

Answer to Problem 9CRP

Explanation of Solution

Check whether the Madison is more reliable using the coefficient of variation.

Explanation of Solution

Check whether it is safe to allocate at least 27 units of Yellowstone River water each year for agricultural and domestic use.

Explanation of Solution

Want to see more full solutions like this?

Chapter 3 Solutions

Check whether there is a guaranteed amount of water the farmers, ranchers, and cities will get from the Yellowstone River each year.

Videos

Check whether there is a guaranteed amount of water the farmers, ranchers, and cities will get from the Yellowstone River each year.

Answer to Problem 9CRP

Explanation of Solution

Find the expected annual flow from the Yellowstone snowmelt. Find the mean, median, and mode.

Answer to Problem 9CRP

Explanation of Solution

Find the range and standard deviation of annual flow.

Answer to Problem 9CRP

Explanation of Solution

Find the 75% Chebyshev interval around the mean.

Answer to Problem 9CRP

Explanation of Solution

Find the five-number summary of the annual water flow. Draw the box-and-whisker plot. Interpret the five-number summary and box-and-whisker plot. Find the values where the middle portion of the data lies. Find the interquartile range. Identify the data outliers.

Answer to Problem 9CRP

Explanation of Solution

Check whether the Madison is more reliable using the coefficient of variation.

Explanation of Solution

Check whether it is safe to allocate at least 27 units of Yellowstone River water each year for agricultural and domestic use.

Explanation of Solution

Want to see more full solutions like this?

Chapter 3 Solutions

Find the expected annual flow from the Yellowstone snowmelt.

Find the mean, median, and mode.

Find the five-number summary of the annual water flow.

Draw the box-and-whisker plot.

Interpret the five-number summary and box-and-whisker plot.

Find the values where the middle portion of the data lies.

Find the interquartile range.

Identify the data outliers.