Question

According to Boeing data, the $757$airliner carries$200$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.

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

b. Assume that half of the $200$passengers are men. What mean doorway height satisfies the condition that there is a $0.95$probability that this height is greater than the mean height of$100$men?

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

Short answer

(a) Mean doorway height is $73.60$inches.

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

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

Step-by-step solution

Given information (part a)

Given in the question that, According to Boeing data, the $757$ airliner carries$200$ 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.

Explanation(part a)

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

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 $2^{\text{nd}}$, 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 $73.60$inches.

Final answer(part a)

Mean doorway height is $73.60$inches.

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 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.

Explanation(part b)

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

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 $2^{\text{nd}}$, 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 $69.46$inches.

Final answer(part b)

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

Given information (part c) 

Given in the question that, According to Boeing data, the$757$airliner carries$200$ 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

Explanation(part c)

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

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

Final answer(part c)

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