An economist uses the price of a gallon of milk as a measure of inflation. She finds that the average price is $3.62 per gallon and the population standard deviation is $0.33. You decide to sample 40...

An economist uses the price of a gallon of milk as a measure of
inflation. She finds that the average price is $3.62 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 $3.28
and $3.86?
c. What is the probability that the difference between the sample
mean and the population mean is less than $0.01?