Show your work.

2. An economist uses the price of a gallon of milk as a measure of inflation.She finds that the average price is $3.50 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? [Hint: use formula in the textbook.]

b) What is the probability that the sample mean is between $3.46 and $3.54? [Remember: the calculation of z will be -/+ the same value, so the probability will be two times the value of one z.]

c) What is the probability that the difference between the sample mean and the population mean is less than $0.01? [Hint: first calculate the price of a gallon at $0.01 -/+ the mean and then calculate the two z's.]

d) What is the likelihood the sample mean is greater than $3.60? [Hint: use the standard mean calculated above in the formula.]