Assume the SAT Mathematics Level 2 test scores are normally distributed with a mean of 400 and a standard deviation of 100. Show all work.

Assume the SAT Mathematics Level 2 test scores are normally distributed with a mean of 400 and a standard deviation of 100. Show all work. Just the answer, without supporting work, will receive no credit.

(a) Consider all random samples of 64 test scores. What is the standard deviation of the sample means? (Round your answer to three decimal places)

(b) What is the probability that 64 randomly selected test scores will have a mean test score that is greater than 425? (Round your answer to four decimal places)