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.)

Question

Mathematics

Rowan Newman

18 April, 12:25

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.)

+5

Answers (1)

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Jaidyn Woodard · 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%