An economist uses the price of a gallon of milk as a measure of inflation. She finds that the average price is $3.82 per gallon and the population standard deviation is $0.33. You decide to sample 40 convenience stores, collect their prices for a gallon of milk, and compute the mean price for the sample.

a. What is the standard error of the mean in this experiment?

b. What is the probability that the sample mean is between $3.78 and $3.86?

c. What is the probability that the difference between the sample mean and the population mean is less than $0.01?

d. What is the likelihood the sample mean is greater than $3.92?