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According to Boeing data, the 757airliner carries200passengers and has doors with a height of 72inches. Assume for a certain population of men we have a mean height of 69.0inches and a standard deviation of 2.8inches.

a. What doorway height would allow 95%of men to enter the aircraft without bending?

b. Assume that half of the 200passengers are men. What mean doorway height satisfies the condition that there is a 0.95probability that this height is greater than the mean height of100men?

c. For engineers designing the 757, which result is more relevant: the height from part a or part b? Why?

Short Answer

Expert verified

(a) Mean doorway height is 73.60inches.

(b) Mean doorway height for the men's is 69.46inches.

(c) The designing the 757airliner doors, the answer of part (a) will be more relevant because it is calculated for the all passengers' height.

Step by step solution

01

Given information (part a)

Given in the question that, According to Boeing data, the 757 airliner carries200 passengers and has doors with a height of72 inches. Assume for a certain population of men we have a mean height of69.0 inches and a standard deviation of 2.8 inches.

02

Explanation(part a)

According to the provided details, for a certain population of men, the mean height of doors is 69inches and the standard deviation is2.8inches.

To estimate the mean doorway height that allows 95%of men to enter aircraft without bending, use the Ti-83 calculator. For this, click on 2nd, then DISTR, and then scroll down to the inverm option and enter the provided details. After this, click on ENTER button on the calculator to have the expected result. The screenshot is given below:

Therefore, mean doorway height is 73.60inches.

03

Final answer(part a)

Mean doorway height is 73.60inches.

04

Given information (part b) 

Given in the question that, According to Boeing data, the 757 airliner carries 200 passengers and has doors with a height of72inches. Assume for a certain population of men we have a mean height of 69.0 inches and a standard deviation of 2.8 inches.

05

Explanation(part b)

According to the provided details, for a certain population of men, the mean height of doors is 69inches and the standard deviation is 2.8inches.

If half of the passengers are men then the standard deviation will be 0.28. To compute the mean doorway height that allows 95%of men to enter aircraft without bending, use the Ti-83 calculator. For this, click on 2nd, then DISTR, and then scroll down to the invnorm option and enter the provided details. After this, click on ENTER button of a calculator to have the desired result. The screenshot is given below:

Therefore, mean doorway height for the men's is 69.46inches.

06

Final answer(part b)

Mean doorway height for the men's is 69.46inches.

07

Given information (part c) 

Given in the question that, According to Boeing data, the757airliner carries200 passengers and has doors with a height of 72 inches. Assume for a certain population of men we have a mean height of 69.0 inches and a standard deviation of 2.8 inches

08

Explanation(part c)

According to the provided details, for a certain population of men, the mean height of doors is 69inches and the standard deviation is 2.8inches.

The designing the 757airliner doors, the answer of part (a) will be more relevant because it is calculated for the all passengers' height.

09

Final answer(part c)

The designing the 757airliner doors, the answer of part (a) will be more relevant because it is calculated for the all passengers' height.

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