In determining automobile mileage ratings, it was found
that the mpg in the city for a certain model is
normally distributed, with a mean of 32 mpg and a standard
deviation of 1.7 mpg. Suppose that the car manufacturer samples
five cars from its assembly line and tests them for mileage
ratings.
a. What is the distribution of the mean mpg for
the sample?
b. What is the probability that the mean mpg of
the sample will be greater than 34 mpg?
c. What is the probability that the mean mpg of
the sample will be less than 30.5 mpg?