Compute the mean and standard deviation of the random variable.

Question

Want to see more full solutions like this?

Answer 1

Question

Chapter 7, Problem 32E

a.

To determine

Compute the mean and standard deviation of the random variable.

a.

Expert Solution

Answer to Problem 32E

The mean of the random variable is 22.

The standard deviation of the random variable is 3.146.

Explanation of Solution

The binomial probability distribution with n=40 and π=0.55 is given.

The mean can be obtained as follows:

μ=nπ=40(0.55)=22

Therefore, the mean of the random variable is 12.5.

The standard deviation of the random variable can be obtained as follows:

σ=nπ(1−π)=40(0.55)(1−0.55)=40(0.55)(0.45)=9.9=3.146

Thus, the standard deviation of the random variable is 3.146.

b.

To determine

Find the probability that X is 25 or greater.

b.

Expert Solution

Answer to Problem 32E

The probability that X takes 25 or greater is 0.2148.

Explanation of Solution

The probability that X is 25 or greater can be obtained as follows:

P(X≥25)=P(X>25−0.5) [Apply the continuity correction factor]=P(X>24.5)=P(X−μσ>24.5−223.146)=P(Z>2.53.146)=P(Z>0.79)

Step-by-step procedure to obtain the probability using MINTAB software:

Choose Graph > Probability Distribution Plot.
Select View Probability.
From Distribution, choose Normal.
Enter Mean as 0 and Standard deviation as 1.
Click the Shaded Area tab.
Define Shaded area by Right tail.
Enter X value as 0.79.
Click OK.

Output obtained using MINITAB software is represented as follows:

STATISTICAL TECHNIQUES FOR BUSINESS AND, Chapter 7, Problem 32E , additional homework tip 1

From the above output, the probability that X takes 25 or more is 0.2148.

c.

To determine

Find the probability that X is 15 or less.

c.

Expert Solution

Answer to Problem 32E

The probability that X takes 15 or less is 0.01970.

Explanation of Solution

The probability that X is 15 or less can be obtained as follows:

P(X≤15)=P(X<15+0.5) [Apply the continuity correction factor]=P(X<15.5)=P(X−μσ<15.5−223.061)=P(Z<−6.53.146)=P(Z<−2.06)

Step-by-step procedure to obtain the probability using MINTAB software:

Choose Graph > Probability Distribution Plot.
Select View Probability.
From Distribution, choose Normal.
Enter Mean as 0 and Standard deviation as 1.
Click the Shaded Area tab.
Define Shaded area by Left tail.
Enter X value as –2.06.
Click OK.

Output obtained using MINITAB software is represented as follows:

STATISTICAL TECHNIQUES FOR BUSINESS AND, Chapter 7, Problem 32E , additional homework tip 2

From the above output, the probability that X takes 15 or less is 0.01970.

d.

To determine

Find the probability that X is between 15 and 25, inclusive.

d.

Expert Solution

Answer to Problem 32E

The probability that X is between 15 and 25 is 0.8578.

Explanation of Solution

The probability that X is between 15 and 25 can be obtained as follows:

P(15≤X≤25)=P(15−0.5<X<25+0.5) [Apply the continuity correction factor]=P(14.5<X<25.5)=P(14.5−223.146<X−μσ<25.5−223.146)=P(−7.53.146<Z<3.53.146)=P(−2.38<Z<1.11)

Step-by-step procedure to obtain the probability using MINTAB software:

Choose Graph > Probability Distribution Plot.
Select View Probability.
From Distribution, choose Normal.
Enter Mean as 0 and Standard deviation as 1.
Click the Shaded Area tab.
Define Shaded area by Middle.
Enter X1 value as –2.38.
Enter X2 value as 1.11.
Click OK.

Output obtained using MINITAB software is represented as follows:

STATISTICAL TECHNIQUES FOR BUSINESS AND, Chapter 7, Problem 32E , additional homework tip 3

From the above output, the probability that X is between 15 and 25 is 0.8578.

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

Please could you explain why 0.5 was added to each upper limpit of the intervals.Thanks

28. (a) Under what conditions do we say that two random variables X and Y are independent? (b) Demonstrate that if X and Y are independent, then it follows that E(XY) = E(X)E(Y); (e) Show by a counter example that the converse of (ii) is not necessarily true.

1. Let X and Y be random variables and suppose that A = F. Prove that Z XI(A)+YI(A) is a random variable.

Answer 2

Question

Chapter 7, Problem 32E

a.

To determine

Compute the mean and standard deviation of the random variable.

a.

Expert Solution

Answer to Problem 32E

The mean of the random variable is 22.

The standard deviation of the random variable is 3.146.

Explanation of Solution

The binomial probability distribution with n=40 and π=0.55 is given.

The mean can be obtained as follows:

μ=nπ=40(0.55)=22

Therefore, the mean of the random variable is 12.5.

The standard deviation of the random variable can be obtained as follows:

σ=nπ(1−π)=40(0.55)(1−0.55)=40(0.55)(0.45)=9.9=3.146

Thus, the standard deviation of the random variable is 3.146.

b.

To determine

Find the probability that X is 25 or greater.

b.

Expert Solution

Answer to Problem 32E

The probability that X takes 25 or greater is 0.2148.

Explanation of Solution

The probability that X is 25 or greater can be obtained as follows:

P(X≥25)=P(X>25−0.5) [Apply the continuity correction factor]=P(X>24.5)=P(X−μσ>24.5−223.146)=P(Z>2.53.146)=P(Z>0.79)

Step-by-step procedure to obtain the probability using MINTAB software:

Choose Graph > Probability Distribution Plot.
Select View Probability.
From Distribution, choose Normal.
Enter Mean as 0 and Standard deviation as 1.
Click the Shaded Area tab.
Define Shaded area by Right tail.
Enter X value as 0.79.
Click OK.

Output obtained using MINITAB software is represented as follows:

STATISTICAL TECHNIQUES FOR BUSINESS AND, Chapter 7, Problem 32E , additional homework tip 1

From the above output, the probability that X takes 25 or more is 0.2148.

c.

To determine

Find the probability that X is 15 or less.

c.

Expert Solution

Answer to Problem 32E

The probability that X takes 15 or less is 0.01970.

Explanation of Solution

The probability that X is 15 or less can be obtained as follows:

P(X≤15)=P(X<15+0.5) [Apply the continuity correction factor]=P(X<15.5)=P(X−μσ<15.5−223.061)=P(Z<−6.53.146)=P(Z<−2.06)

Step-by-step procedure to obtain the probability using MINTAB software:

Choose Graph > Probability Distribution Plot.
Select View Probability.
From Distribution, choose Normal.
Enter Mean as 0 and Standard deviation as 1.
Click the Shaded Area tab.
Define Shaded area by Left tail.
Enter X value as –2.06.
Click OK.

Output obtained using MINITAB software is represented as follows:

STATISTICAL TECHNIQUES FOR BUSINESS AND, Chapter 7, Problem 32E , additional homework tip 2

From the above output, the probability that X takes 15 or less is 0.01970.

d.

To determine

Find the probability that X is between 15 and 25, inclusive.

d.

Expert Solution

Answer to Problem 32E

The probability that X is between 15 and 25 is 0.8578.

Explanation of Solution

The probability that X is between 15 and 25 can be obtained as follows:

P(15≤X≤25)=P(15−0.5<X<25+0.5) [Apply the continuity correction factor]=P(14.5<X<25.5)=P(14.5−223.146<X−μσ<25.5−223.146)=P(−7.53.146<Z<3.53.146)=P(−2.38<Z<1.11)

Step-by-step procedure to obtain the probability using MINTAB software:

Choose Graph > Probability Distribution Plot.
Select View Probability.
From Distribution, choose Normal.
Enter Mean as 0 and Standard deviation as 1.
Click the Shaded Area tab.
Define Shaded area by Middle.
Enter X1 value as –2.38.
Enter X2 value as 1.11.
Click OK.

Output obtained using MINITAB software is represented as follows:

STATISTICAL TECHNIQUES FOR BUSINESS AND, Chapter 7, Problem 32E , additional homework tip 3

From the above output, the probability that X is between 15 and 25 is 0.8578.

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 3

Question

Chapter 7, Problem 32E

a.

To determine

Compute the mean and standard deviation of the random variable.

a.

Expert Solution

Answer to Problem 32E

The mean of the random variable is 22.

The standard deviation of the random variable is 3.146.

Explanation of Solution

The binomial probability distribution with n=40 and π=0.55 is given.

The mean can be obtained as follows:

μ=nπ=40(0.55)=22

Therefore, the mean of the random variable is 12.5.

The standard deviation of the random variable can be obtained as follows:

σ=nπ(1−π)=40(0.55)(1−0.55)=40(0.55)(0.45)=9.9=3.146

Thus, the standard deviation of the random variable is 3.146.

b.

To determine

Find the probability that X is 25 or greater.

b.

Expert Solution

Answer to Problem 32E

The probability that X takes 25 or greater is 0.2148.

Explanation of Solution

The probability that X is 25 or greater can be obtained as follows:

P(X≥25)=P(X>25−0.5) [Apply the continuity correction factor]=P(X>24.5)=P(X−μσ>24.5−223.146)=P(Z>2.53.146)=P(Z>0.79)

Step-by-step procedure to obtain the probability using MINTAB software:

Choose Graph > Probability Distribution Plot.
Select View Probability.
From Distribution, choose Normal.
Enter Mean as 0 and Standard deviation as 1.
Click the Shaded Area tab.
Define Shaded area by Right tail.
Enter X value as 0.79.
Click OK.

Output obtained using MINITAB software is represented as follows:

STATISTICAL TECHNIQUES FOR BUSINESS AND, Chapter 7, Problem 32E , additional homework tip 1

From the above output, the probability that X takes 25 or more is 0.2148.

c.

To determine

Find the probability that X is 15 or less.

c.

Expert Solution

Answer to Problem 32E

The probability that X takes 15 or less is 0.01970.

Explanation of Solution

The probability that X is 15 or less can be obtained as follows:

P(X≤15)=P(X<15+0.5) [Apply the continuity correction factor]=P(X<15.5)=P(X−μσ<15.5−223.061)=P(Z<−6.53.146)=P(Z<−2.06)

Step-by-step procedure to obtain the probability using MINTAB software:

Choose Graph > Probability Distribution Plot.
Select View Probability.
From Distribution, choose Normal.
Enter Mean as 0 and Standard deviation as 1.
Click the Shaded Area tab.
Define Shaded area by Left tail.
Enter X value as –2.06.
Click OK.

Output obtained using MINITAB software is represented as follows:

STATISTICAL TECHNIQUES FOR BUSINESS AND, Chapter 7, Problem 32E , additional homework tip 2

From the above output, the probability that X takes 15 or less is 0.01970.

d.

To determine

Find the probability that X is between 15 and 25, inclusive.

d.

Expert Solution

Answer to Problem 32E

The probability that X is between 15 and 25 is 0.8578.

Explanation of Solution

The probability that X is between 15 and 25 can be obtained as follows:

P(15≤X≤25)=P(15−0.5<X<25+0.5) [Apply the continuity correction factor]=P(14.5<X<25.5)=P(14.5−223.146<X−μσ<25.5−223.146)=P(−7.53.146<Z<3.53.146)=P(−2.38<Z<1.11)

Step-by-step procedure to obtain the probability using MINTAB software:

Choose Graph > Probability Distribution Plot.
Select View Probability.
From Distribution, choose Normal.
Enter Mean as 0 and Standard deviation as 1.
Click the Shaded Area tab.
Define Shaded area by Middle.
Enter X1 value as –2.38.
Enter X2 value as 1.11.
Click OK.

Output obtained using MINITAB software is represented as follows:

STATISTICAL TECHNIQUES FOR BUSINESS AND, Chapter 7, Problem 32E , additional homework tip 3

From the above output, the probability that X is between 15 and 25 is 0.8578.

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 4

Question

Chapter 7, Problem 32E

a.

To determine

Compute the mean and standard deviation of the random variable.

a.

Expert Solution

Answer to Problem 32E

The mean of the random variable is 22.

The standard deviation of the random variable is 3.146.

Explanation of Solution

The binomial probability distribution with n=40 and π=0.55 is given.

The mean can be obtained as follows:

μ=nπ=40(0.55)=22

Therefore, the mean of the random variable is 12.5.

The standard deviation of the random variable can be obtained as follows:

σ=nπ(1−π)=40(0.55)(1−0.55)=40(0.55)(0.45)=9.9=3.146

Thus, the standard deviation of the random variable is 3.146.

b.

To determine

Find the probability that X is 25 or greater.

b.

Expert Solution

Answer to Problem 32E

The probability that X takes 25 or greater is 0.2148.

Explanation of Solution

The probability that X is 25 or greater can be obtained as follows:

P(X≥25)=P(X>25−0.5) [Apply the continuity correction factor]=P(X>24.5)=P(X−μσ>24.5−223.146)=P(Z>2.53.146)=P(Z>0.79)

Step-by-step procedure to obtain the probability using MINTAB software:

Choose Graph > Probability Distribution Plot.
Select View Probability.
From Distribution, choose Normal.
Enter Mean as 0 and Standard deviation as 1.
Click the Shaded Area tab.
Define Shaded area by Right tail.
Enter X value as 0.79.
Click OK.

Output obtained using MINITAB software is represented as follows:

STATISTICAL TECHNIQUES FOR BUSINESS AND, Chapter 7, Problem 32E , additional homework tip 1

From the above output, the probability that X takes 25 or more is 0.2148.

c.

To determine

Find the probability that X is 15 or less.

c.

Expert Solution

Answer to Problem 32E

The probability that X takes 15 or less is 0.01970.

Explanation of Solution

The probability that X is 15 or less can be obtained as follows:

P(X≤15)=P(X<15+0.5) [Apply the continuity correction factor]=P(X<15.5)=P(X−μσ<15.5−223.061)=P(Z<−6.53.146)=P(Z<−2.06)

Step-by-step procedure to obtain the probability using MINTAB software:

Choose Graph > Probability Distribution Plot.
Select View Probability.
From Distribution, choose Normal.
Enter Mean as 0 and Standard deviation as 1.
Click the Shaded Area tab.
Define Shaded area by Left tail.
Enter X value as –2.06.
Click OK.

Output obtained using MINITAB software is represented as follows:

STATISTICAL TECHNIQUES FOR BUSINESS AND, Chapter 7, Problem 32E , additional homework tip 2

From the above output, the probability that X takes 15 or less is 0.01970.

d.

To determine

Find the probability that X is between 15 and 25, inclusive.

d.

Expert Solution

Answer to Problem 32E

The probability that X is between 15 and 25 is 0.8578.

Explanation of Solution

The probability that X is between 15 and 25 can be obtained as follows:

P(15≤X≤25)=P(15−0.5<X<25+0.5) [Apply the continuity correction factor]=P(14.5<X<25.5)=P(14.5−223.146<X−μσ<25.5−223.146)=P(−7.53.146<Z<3.53.146)=P(−2.38<Z<1.11)

Step-by-step procedure to obtain the probability using MINTAB software:

Choose Graph > Probability Distribution Plot.
Select View Probability.
From Distribution, choose Normal.
Enter Mean as 0 and Standard deviation as 1.
Click the Shaded Area tab.
Define Shaded area by Middle.
Enter X1 value as –2.38.
Enter X2 value as 1.11.
Click OK.

Output obtained using MINITAB software is represented as follows:

STATISTICAL TECHNIQUES FOR BUSINESS AND, Chapter 7, Problem 32E , additional homework tip 3

From the above output, the probability that X is between 15 and 25 is 0.8578.

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 7, Problem 32E

a.

To determine

Compute the mean and standard deviation of the random variable.

a.

Expert Solution

Answer to Problem 32E

The mean of the random variable is 22.

The standard deviation of the random variable is 3.146.

Explanation of Solution

The binomial probability distribution with n=40 and π=0.55 is given.

The mean can be obtained as follows:

μ=nπ=40(0.55)=22

Therefore, the mean of the random variable is 12.5.

The standard deviation of the random variable can be obtained as follows:

σ=nπ(1−π)=40(0.55)(1−0.55)=40(0.55)(0.45)=9.9=3.146

Thus, the standard deviation of the random variable is 3.146.

b.

To determine

Find the probability that X is 25 or greater.

b.

Expert Solution

Answer to Problem 32E

The probability that X takes 25 or greater is 0.2148.

Explanation of Solution

The probability that X is 25 or greater can be obtained as follows:

P(X≥25)=P(X>25−0.5) [Apply the continuity correction factor]=P(X>24.5)=P(X−μσ>24.5−223.146)=P(Z>2.53.146)=P(Z>0.79)

Step-by-step procedure to obtain the probability using MINTAB software:

Choose Graph > Probability Distribution Plot.
Select View Probability.
From Distribution, choose Normal.
Enter Mean as 0 and Standard deviation as 1.
Click the Shaded Area tab.
Define Shaded area by Right tail.
Enter X value as 0.79.
Click OK.

Output obtained using MINITAB software is represented as follows:

STATISTICAL TECHNIQUES FOR BUSINESS AND, Chapter 7, Problem 32E , additional homework tip 1

From the above output, the probability that X takes 25 or more is 0.2148.

c.

To determine

Find the probability that X is 15 or less.

c.

Expert Solution

Answer to Problem 32E

The probability that X takes 15 or less is 0.01970.

Explanation of Solution

The probability that X is 15 or less can be obtained as follows:

P(X≤15)=P(X<15+0.5) [Apply the continuity correction factor]=P(X<15.5)=P(X−μσ<15.5−223.061)=P(Z<−6.53.146)=P(Z<−2.06)

Step-by-step procedure to obtain the probability using MINTAB software:

Choose Graph > Probability Distribution Plot.
Select View Probability.
From Distribution, choose Normal.
Enter Mean as 0 and Standard deviation as 1.
Click the Shaded Area tab.
Define Shaded area by Left tail.
Enter X value as –2.06.
Click OK.

Output obtained using MINITAB software is represented as follows:

STATISTICAL TECHNIQUES FOR BUSINESS AND, Chapter 7, Problem 32E , additional homework tip 2

From the above output, the probability that X takes 15 or less is 0.01970.

d.

To determine

Find the probability that X is between 15 and 25, inclusive.

d.

Expert Solution

Answer to Problem 32E

The probability that X is between 15 and 25 is 0.8578.

Explanation of Solution

The probability that X is between 15 and 25 can be obtained as follows:

P(15≤X≤25)=P(15−0.5<X<25+0.5) [Apply the continuity correction factor]=P(14.5<X<25.5)=P(14.5−223.146<X−μσ<25.5−223.146)=P(−7.53.146<Z<3.53.146)=P(−2.38<Z<1.11)

Step-by-step procedure to obtain the probability using MINTAB software:

Choose Graph > Probability Distribution Plot.
Select View Probability.
From Distribution, choose Normal.
Enter Mean as 0 and Standard deviation as 1.
Click the Shaded Area tab.
Define Shaded area by Middle.
Enter X1 value as –2.38.
Enter X2 value as 1.11.
Click OK.

Output obtained using MINITAB software is represented as follows:

STATISTICAL TECHNIQUES FOR BUSINESS AND, Chapter 7, Problem 32E , additional homework tip 3

From the above output, the probability that X is between 15 and 25 is 0.8578.

Answer 6

Chapter 7, Problem 32E

a.

To determine

Compute the mean and standard deviation of the random variable.

a.

Expert Solution

Answer to Problem 32E

The mean of the random variable is 22.

The standard deviation of the random variable is 3.146.

Explanation of Solution

The binomial probability distribution with n=40 and π=0.55 is given.

The mean can be obtained as follows:

μ=nπ=40(0.55)=22

Therefore, the mean of the random variable is 12.5.

The standard deviation of the random variable can be obtained as follows:

σ=nπ(1−π)=40(0.55)(1−0.55)=40(0.55)(0.45)=9.9=3.146

Thus, the standard deviation of the random variable is 3.146.

Answer 7

Chapter 7, Problem 32E

a.

To determine

Compute the mean and standard deviation of the random variable.

Answer 8

a.

Expert Solution

Answer to Problem 32E

The mean of the random variable is 22.

The standard deviation of the random variable is 3.146.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

The binomial probability distribution with n=40 and π=0.55 is given.

The mean can be obtained as follows:

μ=nπ=40(0.55)=22

Therefore, the mean of the random variable is 12.5.

The standard deviation of the random variable can be obtained as follows:

σ=nπ(1−π)=40(0.55)(1−0.55)=40(0.55)(0.45)=9.9=3.146

Thus, the standard deviation of the random variable is 3.146.

Answer 13

b.

To determine

Find the probability that X is 25 or greater.

b.

Expert Solution

Answer to Problem 32E

The probability that X takes 25 or greater is 0.2148.

Explanation of Solution

The probability that X is 25 or greater can be obtained as follows:

P(X≥25)=P(X>25−0.5) [Apply the continuity correction factor]=P(X>24.5)=P(X−μσ>24.5−223.146)=P(Z>2.53.146)=P(Z>0.79)

Step-by-step procedure to obtain the probability using MINTAB software:

Choose Graph > Probability Distribution Plot.
Select View Probability.
From Distribution, choose Normal.
Enter Mean as 0 and Standard deviation as 1.
Click the Shaded Area tab.
Define Shaded area by Right tail.
Enter X value as 0.79.
Click OK.

Output obtained using MINITAB software is represented as follows:

STATISTICAL TECHNIQUES FOR BUSINESS AND, Chapter 7, Problem 32E , additional homework tip 1

From the above output, the probability that X takes 25 or more is 0.2148.

Answer 14

b.

To determine

Find the probability that X is 25 or greater.

Answer 15

b.

Expert Solution

Answer to Problem 32E

The probability that X takes 25 or greater is 0.2148.

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

The probability that X is 25 or greater can be obtained as follows:

P(X≥25)=P(X>25−0.5) [Apply the continuity correction factor]=P(X>24.5)=P(X−μσ>24.5−223.146)=P(Z>2.53.146)=P(Z>0.79)

Step-by-step procedure to obtain the probability using MINTAB software:

Choose Graph > Probability Distribution Plot.
Select View Probability.
From Distribution, choose Normal.
Enter Mean as 0 and Standard deviation as 1.
Click the Shaded Area tab.
Define Shaded area by Right tail.
Enter X value as 0.79.
Click OK.

Output obtained using MINITAB software is represented as follows:

STATISTICAL TECHNIQUES FOR BUSINESS AND, Chapter 7, Problem 32E , additional homework tip 1

From the above output, the probability that X takes 25 or more is 0.2148.

Answer 20

c.

To determine

Find the probability that X is 15 or less.

c.

Expert Solution

Answer to Problem 32E

The probability that X takes 15 or less is 0.01970.

Explanation of Solution

The probability that X is 15 or less can be obtained as follows:

P(X≤15)=P(X<15+0.5) [Apply the continuity correction factor]=P(X<15.5)=P(X−μσ<15.5−223.061)=P(Z<−6.53.146)=P(Z<−2.06)

Step-by-step procedure to obtain the probability using MINTAB software:

Choose Graph > Probability Distribution Plot.
Select View Probability.
From Distribution, choose Normal.
Enter Mean as 0 and Standard deviation as 1.
Click the Shaded Area tab.
Define Shaded area by Left tail.
Enter X value as –2.06.
Click OK.

Output obtained using MINITAB software is represented as follows:

STATISTICAL TECHNIQUES FOR BUSINESS AND, Chapter 7, Problem 32E , additional homework tip 2

From the above output, the probability that X takes 15 or less is 0.01970.

Answer 21

c.

To determine

Find the probability that X is 15 or less.

Answer 22

c.

Expert Solution

Answer to Problem 32E

The probability that X takes 15 or less is 0.01970.

Answer 23

c.

Expert Solution

Answer 24

c.

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

The probability that X is 15 or less can be obtained as follows:

P(X≤15)=P(X<15+0.5) [Apply the continuity correction factor]=P(X<15.5)=P(X−μσ<15.5−223.061)=P(Z<−6.53.146)=P(Z<−2.06)

Step-by-step procedure to obtain the probability using MINTAB software:

Choose Graph > Probability Distribution Plot.
Select View Probability.
From Distribution, choose Normal.
Enter Mean as 0 and Standard deviation as 1.
Click the Shaded Area tab.
Define Shaded area by Left tail.
Enter X value as –2.06.
Click OK.

Output obtained using MINITAB software is represented as follows:

STATISTICAL TECHNIQUES FOR BUSINESS AND, Chapter 7, Problem 32E , additional homework tip 2

From the above output, the probability that X takes 15 or less is 0.01970.

Answer 27

d.

To determine

Find the probability that X is between 15 and 25, inclusive.

d.

Expert Solution

Answer to Problem 32E

The probability that X is between 15 and 25 is 0.8578.

Explanation of Solution

The probability that X is between 15 and 25 can be obtained as follows:

P(15≤X≤25)=P(15−0.5<X<25+0.5) [Apply the continuity correction factor]=P(14.5<X<25.5)=P(14.5−223.146<X−μσ<25.5−223.146)=P(−7.53.146<Z<3.53.146)=P(−2.38<Z<1.11)

Step-by-step procedure to obtain the probability using MINTAB software:

Choose Graph > Probability Distribution Plot.
Select View Probability.
From Distribution, choose Normal.
Enter Mean as 0 and Standard deviation as 1.
Click the Shaded Area tab.
Define Shaded area by Middle.
Enter X1 value as –2.38.
Enter X2 value as 1.11.
Click OK.

Output obtained using MINITAB software is represented as follows:

STATISTICAL TECHNIQUES FOR BUSINESS AND, Chapter 7, Problem 32E , additional homework tip 3

From the above output, the probability that X is between 15 and 25 is 0.8578.

Answer 28

d.

To determine

Find the probability that X is between 15 and 25, inclusive.

Answer 29

d.

Expert Solution

Answer to Problem 32E

The probability that X is between 15 and 25 is 0.8578.

Answer 30

d.

Expert Solution

Answer 31

d.

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

The probability that X is between 15 and 25 can be obtained as follows:

P(15≤X≤25)=P(15−0.5<X<25+0.5) [Apply the continuity correction factor]=P(14.5<X<25.5)=P(14.5−223.146<X−μσ<25.5−223.146)=P(−7.53.146<Z<3.53.146)=P(−2.38<Z<1.11)