Question

Suppose that an airline uses a seat width of 16.9 in. Assume men have hip breadths that are normally distributed with a mean of 14.7 in. and a standard deviation of 1 in. Complete parts​ (a) through​ (c) below.

​(a) Find the probability that if an individual man is randomly​ selected, his hip breadth will be greater than 16.9 in.

The probability is

(b) If a plane is filled with 130 randomly selected​ men, find the probability that these men have a mean hip breadth greater than 16.9 in.

The probability is ______ .

Answer 1

we have

(a) we have to find P(greater than 16.9)

using the probability formula,we can write it as

setting the given values, we get

using the identity

we can write

So, the required probability is 0.0139

(b) This time we have sample size(n) of 130 men, so our calculation will be different

we have to use the formula setting the given values, we get

setting the given values, we get

using the identity

we can write

So, required probability is 0.00

This probability is 0 because 16.9 is outside the 2 standard deviation area of 14.7, where probability is very less.