Customers at a gas station pay with a credit card, debit card, or cash. Assume t

Question

Customers at a gas station pay with a credit card, debit card, or cash. Assume that successive customers make independent choices with P(A) = 0.4, P(B) = 0.2, and P(C) = 0.4. Among the next 100 customers, what are the mean and variance of the number who pay with 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. 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 who use a debit card. Answer part (a) for the number among the 100 who don't pay with cash.

Explanation / Answer

(a)The mean of the number who pay with a debit card is: n*p=100*0.2=20

The variance is: np(1-p)=100*0.20*0.80=16

Because we are interested in whether or not a debit card was used, we can use the binomial distribution. X=number of customers who use a debit card.

(B) The mean of the number who don’t pay with cash is: n*p=100*(1-0.4)=60

The variance is: np(1-p)=100*0.60*0.40=24

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