Please show all work TIA Customers at a gas station pay with a credit card (A),

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Please show all work TIA

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) = 0.4, P(8) = 0.1, and P(C) = 0.5. (a) Among the next 100 customers, what are the mean and variance of the number who pay with a debit card? mean variance customers 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 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 (b) Answer part (a) for the number among the 100 who don't pay with cash mean variance customers customers Need Help?Read ItTalk to a Tutor

Explanation / Answer

(a) Even though there are three options, credit, debit, and cash, since we are only interested in debit vs. non-debit, we have a binomial distribution with n = 100 and p = 0.1(probability of success),

[X=number of customers who use a debit card]

q(probability of failure)=1-p=1-0.1=0.9

Then, the mean =np= 100?0.1 = 10 .

(b) who dont pay with cash So include both credit card and debit card

So p=.4+.1=.5

q=.5

mean=np=100*.5=50

variance=npq=100*.5*.5=25

variance=npq=100 ? 0.1 ? 0.9 = 9

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