Assume the SAT Chemistry Level 2 test scores are normally distributed with a mean of 500 and a standard deviation of 100. (Show all work. Just the answer, without supporting work, will receive no credit.)

(a) If a random sample of 64 test scores is selected, what is the standard deviation of the sample mean?

(b) What is the probability that 64 randomly selected test scores will have a mean test score that is between 475 and 525?