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) = 0.6, P (B) = 0.2, and P (C) = 0.2. (a) Among the next 100 customers, what are the mean and variance of the number who pay with a debit card? mean customers variance customers2 Explain your reasoning. 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 card. Because we are interested in whether or not a debit card was used, we can use the binomial distribution. X = the probability that a customer used a debit card. 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. (b) Answer part (a) for the number among the 100 who don't pay with cash. mean customers variance customers2

Question

Faulkner

Mathematics

6 November, 06:44

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) = 0.6, P (B) = 0.2, and P (C) = 0.2. (a) Among the next 100 customers, what are the mean and variance of the number who pay with a debit card? mean customers variance customers2 Explain your reasoning. 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 card. Because we are interested in whether or not a debit card was used, we can use the binomial distribution. X = the probability that a customer used a debit card. 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. (b) Answer part (a) for the number among the 100 who don't pay with cash. mean customers variance customers2

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Hershey · Answer 1

Step-by-step explanation:

Given that customers at a gas station pay with a credit card (A), debit card (B), or cash (C).

To find out the mean and variance of the number who pay with a debit card for 100 customers

We can sort persons using a debit card or not. Thus there are two outcomes with p = success for each trial = 0.6

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 card out of 100 customers

Mean = np = 60 and variance = npq = 24

Similarly for no of customers do not pay with cash is binomial with p = 0.8

Mean = 80 and variance = 16