Applied Statistics and Probability for Engineers
6th Edition
ISBN: 9781118539712
Author: Douglas C. Montgomery
Publisher: WILEY
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Chapter 6, Problem 135SE
To determine
Check whether there is any meaning full measure of location can be calculated for these data or not.
Find the numerical value.
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A normal distribution has a mean of 50 and a standard deviation of 4. Solve the following three parts?
1. Compute the probability of a value between 44.0 and 55.0.
(The question requires finding probability value between 44 and 55. Solve it in 3 steps.
In the first step, use the above formula and x = 44, calculate probability value.
In the second step repeat the first step with the only difference that x=55.
In the third step, subtract the answer of the first part from the answer of the second part.)
2. Compute the probability of a value greater than 55.0.
Use the same formula, x=55 and subtract the answer from 1.
3. Compute the probability of a value between 52.0 and 55.0.
(The question requires finding probability value between 52 and 55. Solve it in 3 steps.
In the first step, use the above formula and x = 52, calculate probability value.
In the second step repeat the first step with the only difference that x=55.
In the third step, subtract the answer of the first part from the…
If a uniform distribution is defined over the interval from 6 to 10, then answer the followings:
What is the mean of this uniform distribution?
Show that the probability of any value between 6 and 10 is equal to 1.0
Find the probability of a value more than 7.
Find the probability of a value between 7 and 9.
The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be:
More than $27?
Less than or equal to $24?
The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches.
What is the mean amount of rainfall for the month?
What is the probability of less than an inch of rain for the month?
What is the probability of exactly 1.00 inch of rain?
What is the probability of more than 1.50 inches of rain for the month?
The best way to solve this problem is begin by a step by step creating a chart. Clearly mark the range, identifying the…
Client
1
Weight before
diet (pounds)
Weight after
diet (pounds)
128
120
2
131
123
3
140
141
4
178
170
5
121
118
6
136
136
7
118
121
8
136
127
Chapter 6 Solutions
Applied Statistics and Probability for Engineers
Ch. 6.1 - 6-1. Will the sample mean always correspond to one...Ch. 6.1 - 6-2. Will exactly half of the observations in a...Ch. 6.1 - Prob. 3ECh. 6.1 - 6-4. For any set of data values, is it possible...Ch. 6.1 - 6-5. Can the sample standard deviation be equal to...Ch. 6.1 - 6-6. Suppose that you add 10 to all of the...Ch. 6.1 - 6-7. Eight measurements were made on the inside...Ch. 6.1 - Prob. 8ECh. 6.1 - Prob. 9ECh. 6.1 - 6-10. An article in the Journal of Structural...
Ch. 6.1 - Prob. 11ECh. 6.1 - Prob. 12ECh. 6.1 - Prob. 13ECh. 6.1 - 6-14. Preventing fatigue crack propagation in...Ch. 6.1 - 6-15. An article in the Journal of Physiology...Ch. 6.1 - Prob. 16ECh. 6.1 - 6-17. The pH of a solution is measured eight times...Ch. 6.1 - Prob. 18ECh. 6.1 - Prob. 19ECh. 6.1 - Prob. 20ECh. 6.1 - Prob. 21ECh. 6.1 - 6-22. Cloud seeding, a process in which chemicals...Ch. 6.1 - Prob. 23ECh. 6.1 - Prob. 24ECh. 6.2 - 6-25. For the data in Exercise 6-20,
(a) Construct...Ch. 6.2 - 6-26. For the data in Exercise 6-21,
(a) Construct...Ch. 6.2 - Prob. 27ECh. 6.2 - Prob. 28ECh. 6.2 - Prob. 29ECh. 6.2 - 6-30. An article in Technometrics (1977, Vol. 19,...Ch. 6.2 - 6-31. Go Tutorial The following data are the...Ch. 6.2 - Prob. 32ECh. 6.2 - 6-33. The following data represent the yield on 90...Ch. 6.2 - 6-34. Calculate the sample median, mode, and mean...Ch. 6.2 - Prob. 35ECh. 6.2 - Prob. 36ECh. 6.2 - Prob. 37ECh. 6.2 - Prob. 38ECh. 6.2 - Prob. 39ECh. 6.2 - 6-40. An important quality characteristic of water...Ch. 6.2 - Prob. 41ECh. 6.2 - 6-42. A semiconductor manufacturer produces...Ch. 6.2 - Prob. 43ECh. 6.2 - 6-44. In their book Introduction to Linear...Ch. 6.2 - Prob. 45ECh. 6.3 - 6-46. Construct a frequency distribution and...Ch. 6.3 - 6-47. Construct a frequency distribution and...Ch. 6.3 - 6-48. Construct a frequency distribution and...Ch. 6.3 - Prob. 49ECh. 6.3 - 6-50. Construct frequency distributions and...Ch. 6.3 - 6-51. Construct histograms with 8 and 16 bins for...Ch. 6.3 - 6-52. Construct histograms with 8 and 16 bins for...Ch. 6.3 - Prob. 53ECh. 6.3 - 6-54. Construct a histogram for the female student...Ch. 6.3 - 6-55. Construct a histogram for the spot weld...Ch. 6.3 - 6-56. Construct a histogram for the water quality...Ch. 6.3 - Prob. 57ECh. 6.3 - Prob. 58ECh. 6.3 - 6-59. Construct a histogram for the pinot noir...Ch. 6.3 - Prob. 60ECh. 6.3 - Prob. 61ECh. 6.3 - Prob. 62ECh. 6.3 - 6-63. Construct a frequency distribution and...Ch. 6.3 - Prob. 64ECh. 6.4 - 6-65. Using the data on bridge conditions from...Ch. 6.4 - 6-66. Using the data on acid rain from Exercise...Ch. 6.4 - 6-67. Using the data from Exercise 6-22 on cloud...Ch. 6.4 - 6-68. Using the data from Exercise 6-24 on swim...Ch. 6.4 - Prob. 69ECh. 6.4 - Prob. 70ECh. 6.4 - 6-71. The nine measurements that follow are...Ch. 6.4 - Prob. 72ECh. 6.4 - Prob. 73ECh. 6.4 - Prob. 75ECh. 6.4 - Prob. 76ECh. 6.4 - Prob. 77ECh. 6.4 - Prob. 78ECh. 6.4 - Prob. 79ECh. 6.4 - 6-80 In Exercise 6-69, data were presented on the...Ch. 6.4 - 6-81. An article in Nature Genetics...Ch. 6.5 - 6-82. The following data are the viscosity...Ch. 6.5 - Prob. 83ECh. 6.5 - 6-84. In their book Time Series Analysis,...Ch. 6.5 - Prob. 85ECh. 6.5 - Prob. 86ECh. 6.5 - Prob. 87ECh. 6.5 - Prob. 88ECh. 6.5 - Prob. 89ECh. 6.6 - Prob. 90ECh. 6.6 - Prob. 91ECh. 6.6 - 6-92. An article in the Journal of Pharmaceuticals...Ch. 6.7 - 6-93. Construct a normal probability plot of the...Ch. 6.7 - 6-94. Construct a normal probability plot of the...Ch. 6.7 - Prob. 95ECh. 6.7 - 6-96. Construct a normal probability plot of the...Ch. 6.7 - Prob. 97ECh. 6.7 - 6-98. Construct a normal probability plot of the...Ch. 6.7 - Prob. 99ECh. 6.7 - 6-100. Construct a normal probability plot of the...Ch. 6.7 - Prob. 101ECh. 6.7 - Prob. 102ECh. 6 - Prob. 103SECh. 6 - 6-104. The concentration of a solution is measured...Ch. 6 - 6-105. Table 6E.10 shows unemployment data for the...Ch. 6 - 6-106. A sample of six resistors yielded the...Ch. 6 - 6-107. Consider the following two samples:
Sample...Ch. 6 - 6-108. An article in Quality Engineering (1992....Ch. 6 - Prob. 109SECh. 6 - Prob. 110SECh. 6 - Prob. 111SECh. 6 - Prob. 112SECh. 6 - 6-113. Q A manufacturer of coil springs is...Ch. 6 - 6-114. A communication channel is being monitored...Ch. 6 - Prob. 115SECh. 6 - Prob. 116SECh. 6 - 6-117. Construct a normal probability plot of the...Ch. 6 - Prob. 118SECh. 6 - Prob. 119SECh. 6 - Prob. 120SECh. 6 - Prob. 121SECh. 6 - 6-122. In 1789, Henry Cavendish estimated the...Ch. 6 - Prob. 123SECh. 6 - 6-124. Patients arriving at a hospital emergency...Ch. 6 - Prob. 125SECh. 6 - 6-126. The energy consumption for 90 gas-heated...Ch. 6 - Prob. 127SECh. 6 - Prob. 128SECh. 6 - Prob. 129SECh. 6 - Prob. 130SECh. 6 - Prob. 131SECh. 6 - Prob. 132SECh. 6 - Prob. 133SECh. 6 - Prob. 134SECh. 6 - Prob. 135SECh. 6 - Prob. 136SECh. 6 - Prob. 137SE
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- Client 1 Weight before diet (pounds) Weight after diet (pounds) 128 120 2 131 123 3 140 141 4 178 170 5 121 118 6 136 136 7 118 121 8 136 127 a) Determine the mean change in patient weight from before to after the diet (after – before). What is the 95% confidence interval of this mean difference?arrow_forwardIn order to find probability, you can use this formula in Microsoft Excel: The best way to understand and solve these problems is by first drawing a bell curve and marking key points such as x, the mean, and the areas of interest. Once marked on the bell curve, figure out what calculations are needed to find the area of interest. =NORM.DIST(x, Mean, Standard Dev., TRUE). When the question mentions “greater than” you may have to subtract your answer from 1. When the question mentions “between (two values)”, you need to do separate calculation for both values and then subtract their results to get the answer. 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…arrow_forwardIf a uniform distribution is defined over the interval from 6 to 10, then answer the followings: What is the mean of this uniform distribution? Show that the probability of any value between 6 and 10 is equal to 1.0 Find the probability of a value more than 7. Find the probability of a value between 7 and 9. The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be: More than $27? Less than or equal to $24? The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches. What is the mean amount of rainfall for the month? What is the probability of less than an inch of rain for the month? What is the probability of exactly 1.00 inch of rain? What is the probability of more than 1.50 inches of rain for the month? The best way to solve this problem is begin by creating a chart. Clearly mark the range, identifying the lower and upper…arrow_forward
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