The local bakery bakes more than a thousand 1-pound loaves of bread daily, and the weights of these loaves varies. The mean weight is 1 lb. and 1 oz., or 482 grams. Assume the standard deviation of the weights is 18 grams and a sample of 40 loaves is to be randomly selected.

a. This sample of 40 has a mean value of x, which belongs to a sampling distribution. Find the shape of this sampling distribution.

b. Find the mean of this sampling distribution.

c. Find the standard error of this sampling distribution.

d. What is the probability that this sample mean will be between 475 and 495?

e. What is the probability that the sample mean will have a value less than 478?

f. What is the probability that the sample mean will be within 5 grams of the mean?