Question

The air force reports that the distribution of heights of male pilots is approximately normal, with a mean of 72.6 inches and a standard deviation of 2.7 inches. Part A: A male pilot whose height is 74.2 inches is at what percentile? Explain your reasoning and justify your work mathematically. (5 points)

Answer 1

Answer:

Step-by-step explanation:

Given that X -  the distribution of heights of male pilots is approximately normal, with a mean of 72.6 inches and a standard deviation of 2.7 inches.

Height of male pilot = 74.2 inches

We have to find the percentile

X = 74.2

Corresponding Z score = 74.2-72.6 = 1.6

P(X<174.2) = P(Z<1.6) = 0.5-0.4452=0.0548=5.48%

i.e. only 5% are below him in height.

Thus the malepilot is in 5th percentile.