PRACTICE OF STATS - 1 TERM ACCESS CODE
PRACTICE OF STATS - 1 TERM ACCESS CODE
4th Edition
ISBN: 9781319403348
Author: BALDI
Publisher: Macmillan Higher Education
Question
Book Icon
Chapter 11, Problem 11.8AYK

(a)

To determine

To use the technology of your choice to find the proportion of observations from a standard normal distribution and also sketch a standard normal curve and shade the area.

(a)

Expert Solution
Check Mark

Answer to Problem 11.8AYK

The proportion of observations for z<2.85 is 0.99781 .

Explanation of Solution

It is given that we have to use the technology of choice to find the proportion of observations from a standard normal distribution so, we will use excel function to solve the probability. The function used is as:

  =NORM.S.DIST(z,cumulative)

Thus, we have to find the probability for z<2.85 , then the calculation is as:

    For z<2.85=NORM.S.DIST(2.85,TRUE)

The result is as:

    For z<2.850.99781

Therefore, the proportion of observations for z<2.85 is 0.99781 .

And the sketch for the following is as:

  PRACTICE OF STATS - 1 TERM ACCESS CODE, Chapter 11, Problem 11.8AYK , additional homework tip  1

(b)

To determine

To use the technology of your choice to find the proportion of observations from a standard normal distribution and also sketch a standard normal curve and shade the area.

(b)

Expert Solution
Check Mark

Answer to Problem 11.8AYK

The proportion of observations for z>2.85 is 0.002186 .

Explanation of Solution

It is given that we have to use the technology of choice to find the proportion of observations from a standard normal distribution so, we will use excel function to solve the probability. The function used is as:

  =NORM.S.DIST(z,cumulative)

Thus, we have to find the probability for z>2.85 , then the calculation is as:

    For z>2.85=1-NORM.S.DIST(2.85,TRUE)

The result is as:

    For z>2.850.002186

Therefore, the proportion of observations for z>2.85 is 0.002186 .

And the sketch for the following is as:

  PRACTICE OF STATS - 1 TERM ACCESS CODE, Chapter 11, Problem 11.8AYK , additional homework tip  2

(c)

To determine

To use the technology of your choice to find the proportion of observations from a standard normal distribution and also sketch a standard normal curve and shade the area.

(c)

Expert Solution
Check Mark

Answer to Problem 11.8AYK

The proportion of observations for z>1.66 is 0.95154 .

Explanation of Solution

It is given that we have to use the technology of choice to find the proportion of observations from a standard normal distribution so, we will use excel function to solve the probability. The function used is as:

  =NORM.S.DIST(z,cumulative)

Thus, we have to find the probability for z>1.66 , then the calculation is as:

    For z>-1.66=1-NORM.S.DIST(-1.66,TRUE)

The result is as:

    For z>-1.660.95154

Therefore, the proportion of observations for z>1.66 is 0.95154 .

And the sketch for the following is as:

  PRACTICE OF STATS - 1 TERM ACCESS CODE, Chapter 11, Problem 11.8AYK , additional homework tip  3

(d)

To determine

To use the technology of your choice to find the proportion of observations from a standard normal distribution and also sketch a standard normal curve and shade the area.

(d)

Expert Solution
Check Mark

Answer to Problem 11.8AYK

The proportion of observations for 1.66<z<2.85 is 0.94936 .

Explanation of Solution

It is given that we have to use the technology of choice to find the proportion of observations from a standard normal distribution so, we will use excel function to solve the probability. The function used is as:

  =NORM.S.DIST(z,cumulative)

Thus, we have to find the probability for 1.66<z<2.85 , then the calculation is as:

    For -1.66=NORM.S.DIST(2.85,TRUE)-NORM.S.DIST(-1.66,TRUE)

The result is as:

    For -1.660.949356

Therefore, the proportion of observations for 1.66<z<2.85 is 0.94936 .

And the sketch for the following is as:

  PRACTICE OF STATS - 1 TERM ACCESS CODE, Chapter 11, Problem 11.8AYK , additional homework tip  4

(e)

To determine

To explain in your words why these proportions can also be considered probabilities.

(e)

Expert Solution
Check Mark

Explanation of Solution

As we know that these are the probabilities as they satisfy all the three conditions that are:

For any event A P(A)0 .

Probability of sample space i.e. total probability is one and total area under curve is also one.

If A1,A2,A3 are disjoint events then P(A1UA2UA3U....)=P(A1)+P(A2)+P(A3)+.. .

Thus, if all the above three conditions are satisfied then these proportions can also be considered probabilities.

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!
Students have asked these similar questions
Can you help me solve  problem 38 with steps im stuck.
How do the samples hold up to the efficiency test? What percentages of the samples pass or fail the test? What would be the likelihood of having the following specific number of efficiency test failures in the next 300 processors tested? 1 failures, 5 failures, 10 failures and 20 failures.
The battery temperatures are a major concern for us. Can you analyze and describe the sample data? What are the average and median temperatures? How much variability is there in the temperatures? Is there anything that stands out? Our engineers’ assumption is that the temperature data is normally distributed. If that is the case, what would be the likelihood that the Safety Zone temperature will exceed 5.15 degrees? What is the probability that the Safety Zone temperature will be less than 4.65 degrees? What is the actual percentage of samples that exceed 5.25 degrees or are less than 4.75 degrees? Is the manufacturing process producing units with stable Safety Zone temperatures? Can you check if there are any apparent changes in the temperature pattern? Are there any outliers? A closer look at the Z-scores should help you in this regard.
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Text book image
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Text book image
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Text book image
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
Text book image
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Text book image
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman