Question

Customers at a gas station pay with a credit card (A), debit card (8), or cash (C). Assume that successive customers make independent choices with P(A) = 0.4, P(B) 0.2, and P(C) = 0.4. (a) Among the next 100 customers, what are the mean and variance of the number who pay with a debit card? customers customers Explain your reasoning. O Because we are interested in whether or not a debit card was used, we can use the binomial distribution. Xthe probability that a customer used a debit Because we are interested in whether or not a debit card was used, we can use the binomial distribution. X- the number of customers at the gas station. Because we are interested in whether or not a debit card was used, we can use the binomial distribution. X the number of customers who use a debit (b) Answer part (a) for the number among the 100 who don't pay with cash. customers vanance

Answer 1

a) mean = n * p

             = 100 * 0.2 = 20

variance = n * p * (1 - p)

             = 100 * 0.2 * 0.8 = 16

b) P(c') = 1 - 0.4 = 0.6

mean = 100 * 0.6 = 60

variance = n * p * (1 - p)

             = 100 * 0.6 * 0.4 = 24