# A survey found that women’s heights are normally distributed with mean . and standard deviation . The survey also found that men’s heights are normally distributed with mean . and standard deviation . Consider an executive jet that seats six with a doorway height of

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20.

A survey found that women’s heights are normally distributed with mean . and standard deviation . The survey

also found that men’s heights are normally distributed with mean . and standard deviation . Consider an

executive jet that seats six with a doorway height of . Complete parts (a) through (c) below.

63.6 in 3.4 in

68.7 in 3.8 in

56 in

a. What percentage of adult men can fit through the door without bending?

The percentage of men who can fit without bending is 0.04 %.

(Round to two decimal places as needed.)

b. Does the door design with a height of 56 in. appear to be adequate? Why didn’t the engineers design a larger door?

A. The door design is adequate, because although many men will not be able to fit without bending, most

women will be able to fit without bending. Thus, a larger door is not needed.

B. The door design is adequate, because the majority of people will be able to fit without bending. Thus, a

larger door is not needed.

C. The door design is inadequate, because every person needs to be able to get into the aircraft without

bending. There is no reason why this should not be implemented.

D. The door design is inadequate, but because the jet is relatively small and seats only six people, a much

higher door would require major changes in the design and cost of the jet, making a larger height not

practical.

c. What doorway height would allow 40% of men to fit without bending?

The doorway height that would allow 40% of men to fit without bending is 67.7 in.

(Round to one decimal place as needed.)

YOU ANSWERED: C.

0.07

Assume that military aircraft use ejection seats designed for men weighing between lb and lb. If women’s

weights are normally distributed with a mean of lb and a standard deviation of lb, what percentage of women

have weights that are within those limits? Are many women excluded with those specifications?

138.8 217

162.4 40.8

The percentage of women that have weights between those limits is %.

(Round to two decimal places as needed.)

Are many women excluded with those specifications?

A. Yes, the percentage of women who are excluded, which is equal to the probability found previously,

shows that about half of women are excluded.

B. No, the percentage of women who are excluded, which is the complement of the probability found

previously, shows that very few women are excluded.

C. No, the percentage of women who are excluded, which is equal to the probability found previously,

shows that very few women are excluded.

D. Yes, the percentage of women who are excluded, which is the complement of the probability found

previously, shows that about half of women are excluded.

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21.

19: Standard Normal Table (Page 1)

Assume that human body temperatures are normally distributed with a mean of 98.21°F and a standard deviation of 0.64°F.

a. A hospital uses as the lowest temperature considered to be a fever. What percentage of normal and healthy

persons would be considered to have a fever? Does this percentage suggest that a cutoff of is appropriate?

100.6°F

100.6°F

b. Physicians want to select a minimum temperature for requiring further medical tests. What should that temperature be, if

we want only 5.0% of healthy people to exceed it? (Such a result is a false positive, meaning that the test result is positive,

but the subject is not really sick.)

Click to view page 1 of the table. Click to view page 2 of the table. 19 20

a. The percentage of normal and healthy persons considered to have a fever is %.

(Round to two decimal places as needed.)

Does this percentage suggest that a cutoff of 100.6°F is appropriate?

A. Yes, because there is a small probability that a normal and healthy person would be considered to have

a fever.

B. Yes, because there is a large probability that a normal and healthy person would be considered to have

a fever.

C. No, because there is a small probability that a normal and healthy person would be considered to have

a fever.

D. No, because there is a large probability that a normal and healthy person would be considered to have

a fever.

b. The minimum temperature for requiring further medical tests should be if we want only 5.0% of

healthy people to exceed it.

°F

(Round to two decimal places as needed.)

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20: Standard Normal Table (Page 2)

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22.

21: Standard Normal Table (Page 1)

The lengths of pregnancies are normally distributed with a mean of days and a standard deviation of da

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