Historically, 65% of customers who have entered a store have made a purchase (each customer can make only a single purchase). The average purchase for these customers is $205.00. If on a particular day, 512 customers visit a store, calculate the following (assuming that each customer is equally likely to make a purchase):
a. Probability that more than 314 customers will make a purchase
b. Probability than no more than 310 customers will make a purchase
c. Probability that between 320 (inclusive) and 325 (inclusive) purchases will be made.
d. What is the probability that EXACTLY 305 customers will make a purchase?