6. -5 points Customers at a gas station pay with a credit card (A), debit card (

Question

6. -5 points 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 PIA)- 0.5, P(B) 0.2, and PC) 0.3. (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 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. 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. meán variance customers customers2 Need Help? Read It Talk to a Tutor Submit Answer Save ProgressPractice Another Version

Explanation / Answer

a.) 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.

so , n=100 ,p=0.2 , q=1-p=1-0.2=0.8

Mean= n*p = 100*0.2= 20

Variance= n*p*q= 100*0.2*0.8 = 16

b.) Here n=100 , p=0.7 , q=1-p=1-0.7=0.3

Mean= n*p= 100*0.7=70

Variance= n*p*q= 100*0.7*0.3=21

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