Question

An airliner carries 100 passengers and has doors with a height of 76 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8in.

a. If a male passenger is randomly​ selected, find the probability that he can fit through the doorway without bending.
​(Round to four decimal places as​ needed.)

Answer 1

First let us calculate for the z score using the formula:

z = (x – u) / s

where u is the mean height of men = 69 in, x is the height of the door = 76, and s is the standard deviation = 2.8 in

z = (76 – 69) / 2.8

z = 2.5

From the standard probability table, at z = -2.5 the probability P is:

P = 0.9938 = 99.38%