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

Mathematics

Izabelle Herman

31 March, 19:11

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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Bria Short · 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