Suppose that the average weekly earnings for employees in general automotive repair shops is $450, and that the standard deviation for the weekly earnings for such employees is $50. A sample of 100 such employees is selected at random.

(1) Find the mean and standard deviation of the sampling distribution of the average weekly earnings in the sample. (4 points)

(2) What's the shape or kind of distribution is this sampling distribution of the average weekly earnings? (2 points)

(3) Find the probability that the mean of the sample is between $445 and $455. (2 points)

(4) Find the probability that the mean of the sample is smaller than $460. (2 points)