Solution Found!
Customers at a gas station pay with a credit card (A),
Chapter 4, Problem 65E(choose chapter or problem)
Customers at a gas station pay with a credit card (A), debit card (B), or cash (C). Assume that successive customers make independent choices, with P(A) = .5, P(B) = .2 and P(C) = .3. a. ?Among the next 100 customers, what are the mean and variance of the number who pay with a debit card? Explain your reasoning. b.?? nswer part (a) for the number among the 100 who don’t pay with cash.
Questions & Answers
QUESTION:
Customers at a gas station pay with a credit card (A), debit card (B), or cash (C). Assume that successive customers make independent choices, with P(A) = .5, P(B) = .2 and P(C) = .3. a. ?Among the next 100 customers, what are the mean and variance of the number who pay with a debit card? Explain your reasoning. b.?? nswer part (a) for the number among the 100 who don’t pay with cash.
ANSWER:Answer : Step 1 of 2 : Given, Customers at a gas station pay with a credit card (A), debit card (B), or cash (C). Assume that successive customers make independent choices, with P(A) = .5, P(B) = .2 and P(C) = .3. a) Among the next 100 customers. The claim is to find the mean and variance of the number who pay with a debit card( that is P(B) = 0.2) Mean of binomial distribution is np and variance is npq Where n = 100, p = 0.8 and q = 1 - p = 0.8 Mean = np = 100 (0.20) = 20 Variance = npq = 100 (0.2)(0.8) = 16 Therefore, mean = 20 and variance = 16