Thirty percent of all customers who enter a store will make a purchase. Suppose that six customers enter the store and that these customers make independent purchase decisions.

a. Let x the number of the six customers who will make a purchase. Write the binomial formula for this situation.

b. Use the binomial formula to calculate

(1) The probability that exactly five customers make a purchase.

(2) The probability that at least three customers make a purchase.

(3) The probability that two or fewer customers make a purchase.

(4) The probability that at least one customer makes a purchase.