Question

Suppose that an airline uses a seat width of 16.5 in. Assume men have hip breadths that are normally distributed with a mean of 14.6 in. and a standard deviation of 1 in. Complete parts​ (a) through​ (b) below. ​(a) Find the probability that if an individual man is randomly​ selected, his hip breadth will be greater than 16.5 in. The probability is ​(Round to four decimal places as​ needed.) ​(b) If a plane is filled with 126 randomly selected​ men, find the probability that these men have a mean hip breadth greater than 16.5 in.The probability is ​(Round to four decimal places as​ needed.)

Answer 1

Let X is a random variable shows the hip breadth. Here X has normal distribution with parameters as follows:

(a)

The z-score for X = 16.5 is

The probability that if an individual man is randomly​ selected, his hip breadth will be greater than 16.5 in is

P(X > 16.5) = P(z > 1.9) = 1 - P(z <= 1.9) = 1 - 0.9713 = 0.0287

Answer:0.0287

(b)

The z-score for is

The probability that these men have a mean hip breadth greater than 16.5 in is