Acertain 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?

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%.

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