6. 15 points My Notes Ask Your Teach Customers at a gas station pay with a credi

Question

6. 15 points My Notes Ask Your Teach 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) 0.5, P(B)0.3, 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 customers2 variance Explain your reasoning. O 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. O 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. O 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. (b) Answer part (a) for the number among the 100 who don't pay with cash mean customers variance customers Need Help? Talk to Tuter

Explanation / Answer

(a)

Here because we are interested in whether or not debit card was used, we make use of the binomial distribution with the following parameters:

n = 100, p = 0.3

X = number of customers who use a debit card

So,

mean = E[X] = n*p = 100*0.3 = 30

Variance = Var(X) = n*p*(1-p) = 100*0.3*0.7 = 21

The correct option for reasoning is option 2.

(b)

Here we are interested in whether or not cash was used, we make use of the binomial distribution with the following parameters:

n = 100, p = 1-0.2 = 0.8

mean = n*p = 100*0.8 = 80

Variance = n*p*(1-p) = 100*0.8*0.2 = 16.

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