7.9 Buying a car A car dealer offers a $500 discount to customers if they agree to buy a car immediately without doing further research. Suppose 30% of all customers who visit him accept this offer. Depending on whether or not a given customer accepts the offer, let X be either 1 or 0, respectively.

a. If n = 5 customers, find the probability distribution of the proportion of customers who will accept the offer.

(Hint: List all possible values for the sample proportion and their chances of occurring.)

b. Referring to part

a, what are the mean and standard deviation of the sample proportion?

c. Repeat part b for a group of n = 10 customers and n = 100 customers.

d. What happens to the mean and standard deviation of the sample proportion as n increases?