Suppose that cars arrive at Burger King’s drive-through at the rate of 20 cars every hour between 12:00 noon and 1:00 P.M. A random sample of 40 one-hour time periods between 12:00 noon and 1:00 P.M. is selected and has 22.1 as the mean number of cars arriving.

(a) Why is the sampling distribution of x approximately normal?

(b) What is the mean and standard deviation of the sampling distribution of x̄ assuming that µ = 20 and σ = √20?

(c) What is the probability that a simple random sample of 40 one-hour time periods results in a mean of at least 22.1 cars?

Is this result unusual? What might we conclude?