÷ÈÓ°Ö±²¥

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

The mean height is $69.0$inches.

The standard deviation is$2.8$inches.

According to the information, We observed that:

Men with height $\mathrm{μ}=69$

Standard deviation $\mathrm{σ}=2.8$

We can use Ti-83 calculator to find the ${95}^{th}$percentile:

Therefore,

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

Hence, mean doorway height is$73.60$inches

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

The mean height is $69.0$inches.

The standard deviation is $2.8$inches.

The standard deviation is $2.8$ based on the information provided.

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

${\mathrm{σ}}_{\mathrm{X}}=\frac{\mathrm{σ}}{\sqrt{n}}$

$=\frac{2.8}{10}$

$=0.28$

Hence, the ${95}^{th}$percentile$=invNorm(0.95,69,0.28)=69.46$

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

The engineers designing the$757$, 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.