15. -/5 points DevoreStat8 3.E.065. My Notes Customers at a gas station pay with

Question

15. -/5 points DevoreStat8 3.E.065. My Notes 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 PA)-0.5, P B) 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 variance customers customers2 Explain your reasoning. Because we are interested in whether or not a debit card was used, we can use the binomial distribution. Xthe number of customers at the gas station 0 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 we canuse the binomiai distiui (b) Answer part (a) for the number among the 100 who don't pay with cash. mean variance customers customers2 Need Help? ReadIt Read It

Explanation / Answer

a) This is an instance of binomial distribution. Therefore, mean, E(X)=np=100*0.3=30 Var(X)=npq=100*0.3*0.7=21

b) Option 2. Binomial distribution uses the formula, P(X,r,p)=nCr(p)^r(q)^n-r, where, X denotes the number of success, here customers wh uses debit card.

c) The mean is r/p=100/0.2=500 Variance=r(1-p)/p^2=100(1-0.2)/0.2^2=2000

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