Question: The manager of a retail store knows that 7% of all checks written are "hot" checks. Of the next 150 checks written at the retail store, find the following probabilities:

a. What is the exact probability that more than 20 checks are hot?

b. Let X be the number of the hot checks found in a random sample of 150 checks. Determine the mean ( \(\mu \) ) and standard deviation ( \(\sigma \) ) of X and then find the exact probability that X will fall within the limits of \(\mu \) ± \(2\sigma \)