An airliner carries 300 passengers and has doors with a height of 75 inches heights of men are normally distributed with a mean of 69 inches and a standard deviation of 2.8 inches female passenger is randomly selected find the probability that you can fit through the door way without bending

Complete Question

An airliner carries 300 passengers and has doors with a height of 75 inches. Heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. 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.)

0.9839

Step-by-step explanation:

We solve using formula Z score

z = (x-μ)/σ,

where

x is the raw score

μ is the population mean

σ is the population standard deviation.

We are to find thethe probability that he can fit through the doorway without bending. This means his height is less than (< ) the height of the doorway(75 inches).

z = 75 - 69/2.8

z = 2.14286

Probability value from Z-Table:

P(x ≤ 75) = P(x = 75) = P(x < 75)

= 0.98394

Approximately ≈ 0.9839