Question

Southwest airlines uses a boeing 737 for some of its flights and that aircraft seats 122 passengers. if the plane is full with 122 randomly selected men find the probabability that these men have a mean hip breadth greater than 17 inches.

Answer 1

Assuming that the mean hip breadths are normallty distributed with mean equal to 'm' and standard deviation equal to 'S'.

Data given to us is:

Sample size, n = 122

First we calculate the standard error of mean, which is:

SE = S/(n^0.5) = S/(122^0.5) = S/11.05

Let X denote the mean hip width of these randomly selected men.

Now we calculate z-statistic:

z = (X-m)/SE = (17-m)/(S/11.05) = z'

So, the probability that these men have a mean hip breadth greater than 17 inches is:

P(X > 17) = P(z > z')

First we calculate z', by assuming the following values:

m = 15.1, S = 1.1

So,

z' = (17-m)/(S/11.05) = (17-15.1)/1.1/11.05) = 0.156

So, looking at the cumulative z-table, we have:

P(z > 0.156) = 0.438