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In Exercises, use these parameters (based on Data Set 1):•

Chapter 6, Problem 21BSC

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QUESTION:

In Exercises 21–24, use these parameters (based on Data Set 1 in Appendix B):

• Men's heights are normally distributed with mean 69.5 in. and standard deviation 2.4 in.

• Women's heights are normally distributed with mean 63.8 in. and standard deviation 2.6 in.

Navy Pilots The U.S. Navy requires that fighter pilots have heights between 62 in. and 78 in.

a. Find the percentage of women meeting the height requirement. Are many women not qualified because they are too short or too tall?

b. Find the percentage of men meeting the height requirement. Are many men not qualified because they are too short or too tall?

c. If the Navy changes the height requirements so that all women are eligible except the shortest 2% and the tallest 2%, what are the new height requirements for women?

d. If the Navy changes the height requirements so that all men are eligible except the shortest 1% and the tallest 1%, what are the new height requirements for men?

Questions & Answers

QUESTION:

In Exercises 21–24, use these parameters (based on Data Set 1 in Appendix B):

• Men's heights are normally distributed with mean 69.5 in. and standard deviation 2.4 in.

• Women's heights are normally distributed with mean 63.8 in. and standard deviation 2.6 in.

Navy Pilots The U.S. Navy requires that fighter pilots have heights between 62 in. and 78 in.

a. Find the percentage of women meeting the height requirement. Are many women not qualified because they are too short or too tall?

b. Find the percentage of men meeting the height requirement. Are many men not qualified because they are too short or too tall?

c. If the Navy changes the height requirements so that all women are eligible except the shortest 2% and the tallest 2%, what are the new height requirements for women?

d. If the Navy changes the height requirements so that all men are eligible except the shortest 1% and the tallest 1%, what are the new height requirements for men?

ANSWER:

Problem 21BSC

Answer:

Step1 of 4:

We have,

• Men’s heights are normally distributed with mean 69.5 in. and standard deviation 2.4 in.

• Women’s heights are normally distributed with mean 63.8 in. and standard deviation 2.6 in.The U.S. Navy requires that fighter pilots have heights between 62 in. and 78 in.

Step2 of 4:

We need to find

a. Find the percentage of women meeting the height requirement. Are many women not qualified because they are too short or too tall?

b. Find the percentage of men meeting the height requirement. Are many men not qualified because they are too short or too tall?

c. If the Navy changes the height requirements so that all women are eligible except the shortest 2% and the tallest 2%, what are the new height requirements for women?

d. If the Navy changes the height requirements so that all men are eligible except the shortest 1% and the tallest 1%, what are the new height requirements for men?

Step3 of 4:

a).

Let us assume that X be the women’s height  

As per given information mean and standard deviation of women’s height  is  and

Now,

The percentage of women meeting the height between 62 in. and 78 in. is given by

P(6278) = P[]

                         = P(-0.69 Z 5.46)

                         = P(5.46) - P(-0.69)

                         = 0.999 - 0.2451

                         = 0.7549

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