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 30 mpg and a standard deviation of 1.0 mpg. Suppose that the car manufacturer samples 5 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 sample mean will be greater than 31 mpg?
c. What is the probability that the sample mean will be less than 29.5 mpg?
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