Past experience indicates that 40% of all individuals entering a certain store decide to make a purchase. Exactly 20 customers enter the store every hour. The manager of the store tells the worker to record the number of customers making a purchase every hour. Let the random variable = number of customers making a purchase in 1 hour.

a. What is the distribution of ? Include parameter values. (This is the population distribution.)

b. What is the mean () and the standard deviation () of ?

c. The worker will record this number every hour for next 10 hours. What is the sample? What is the sample size? (This is different from the number of trials for the population distribution.)

d. What is the distribution of the mean number of customers making a purchase per hour over the next 10 hours ()? (Hint: Use central limit theorem.)

e. What is the probability that the worker will observe more than 9 customers making a purchase per hour on average over the next 10 hours?