A large mail sorting center finds that, on average, 0.5% of all letters have an incorrect address.

a. What is the probability that in a random sample of 500 letters at the center exactly 5 letters have an incorrect address?
b. What is the probability that the random variable x, where x = Number of letters with an incorrect address, will exceed its mean by more than 2 standard deviations in a random sample of 500 letters?