Question

An airliner carries 350 passengers and has doors with ah height of 72 in. Heights of men are normally distributed with a mean of 69.0 in. and a standard deviation of 2.8 on. Complete parts a through d.a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending.The probability is_____.

Answer 1

Answer:

P ( Z < 72 ) = 0.8577     or   P ( Z < 72 ) = 85.77 %

Step-by-step explanation:

We know:

-A normal distribution

-Mean      μ =   69.0   in

-Standard deviation      σ  = 2.8   in

- Population    n  =  350

And doors height   72 in

If passengers will pass through the door without bending that means he must be under 72 in tall, therefore we are looking for the probability of men under 72 in, to find such probability we compute the value of Z according to

Z  =  ( X - μ ) / σ     ⇒             Z  =  ( 72 - 69 ) / 2.8

Z  = 1.07

Now with this value we look the Z tables, to find a value of: 0.8577

So the probability of select a men and that he can fit through the door is

P ( Z < 72 ) = 0.8577  or    P ( Z < 72 ) =  85.77 %