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According to Boeing data, the 757airliner carries 200passengers 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 2.8 inches.
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 a0.95probability that this height is greater than the mean height of 100men?

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) The mean doorway height to enter the aircraft without bending is73.60inches.
(b) The mean doorway height for the men is 69.46inches.

(c) The result for the height from part (a) is more relevant.

Step by step solution

01

Part (a) Step 1: Given information 

Given in the question that, the 757 airliner carries 200 passengers and has doors with a height of 72 inches.

The mean height is 69.0inches.

The standard deviation is2.8inches.

02

Part (a) Step 2: Explanation 

According to the information, We observed that:

Men with height μ=69

Standard deviation σ=2.8

We can use Ti-83 calculator to find the 95thpercentile:

Therefore,

The 95th percentile =invNorm(0.95,69,2.8)=73.6

Hence, mean doorway height is73.60inches

03

Part (b) Step 1: Given information

Given in the question that, the 757 airliner carries 200 passengers and has doors with a height of 72 inches.

The mean height is 69.0inches.

The standard deviation is 2.8inches.

04

Part (b) Step 2: Explanation 

The standard deviation is 2.8 based on the information provided.

If half of the passengers are men, the standard deviation will be:

σX=σn

=2.810

=0.28

Hence, the 95thpercentile=invNorm(0.95,69,0.28)=69.46

05

Part (c) Step 1: Given information 

The 757airliner carries 200passengers and has doors with a height of 72 inches.

06

Part (c) Step 2: Explanation

The engineers designing the757, the result from part (a) will be more relevant comparing to part (b), because that is calculated for all passengers' height.

So the result from part (a) is more relevant.

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