Solution Found!
Answer: Customers at a gas station pay with a credit card
Chapter 3, Problem 65E(choose chapter or problem)
Problem 65E
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. Answer part (a) for the number among the 100 who don’t pay with cash.
Questions & Answers
QUESTION:
Problem 65E
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. Answer 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.
- 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