Question

A certain car model has a mean gas mileage of 31 miles per gallon (mpg) with a standard deviation 3 mpg. a pizza delivery company buys 35 of these cars. what is the probability that the average mileage of the fleet is between 30.9 and 31.2 mpg?

Answer 1

We assume that the "population" mean and std. dev. are 31 mpg and 3 mpg respectively. Here we're working with a SAMPLE of size 35, which has mean 31 mpg and std. dev. (3/sqrt(35)) mpg (if I remember this formula correctly).

This comes out to sample mean 31 mpg and sample std. dev. 0.507 mpg.

Using a calculator to find the area under the std. norm. curve between 30.9 and 31.2 mpg, I get

normalcdf(30.9,31.2,31,0.507) = 0.232.

So the probability that the average mileage of the fleet is between 30.9 and 31.2 mpg is 0.232, or about 23%.