A survey by Statistics Canada shows the average household expenditure on post-secondary textbooks is $53.00, with a

Question:

A survey by Statistics Canada shows the average household expenditure on post-secondary textbooks is $53.00, with a standard deviation of $18.61. A similar poll randomly selects 150 households to find average expenditure on post-secondary textbooks.
a. Find the probability that the mean is greater than $57.00.
b. If a sample of 150 households does yield a mean of $57.00 or greater, is there reason to believe that this sample came from a population with a mean that is higher than $53.00?