Question

An airliner carrier 400 passengers and has doors 75 inches height of men are normally distributed with a mean of 69 and a standard deviation of 2.8 is half of the 400 passengers are men find the probability that the mean height of 200 man is less than 75 inches?

Answer 1

Solution:

Let X be a random variable which represents the height of male passengers of an airline carrier.

Given that, X ~ N(69, 2.82)

i.e. μ = 69 inches, σ = 2.8 inches

We have to find P(x̄ < 75).

(Where, x̄ is mean height of 200 men).

We know that if X ~ N(μ, σ​​​​​​2) then x̄ ~ N(μ, σ​​​​​​2/n)

And if x̄ ~ N(μ, σ​​​​​​2/n) then

(Where, x̄ is sample mean and n is sample size.)

We have, n = 200 , μ = 69 inches, σ = 2.8 inches

Using "pnorm" function of R we get, P(Z < 30.30) = 1.0000

The probability that the mean height of 200 man is less than 75 inches is 1.0000.