Customers at a gas station pay with a credit card (A), debit card (B), or cash (

Question

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) = 0.6, P(B) = 0.2, 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 variance customers^2 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 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. mean customers variance customers^2

Explanation / Answer

a)

here proportion of those who pays with debit card=P(B)=p=0.2

n=100

mean =np=100*0.2=20

variance=np(1-p)=100*0.2*(1-0.2)=16

because we are interested in weather or not a debit card is used, we can use the binomial distribution,X =the number of customers who use a debit card,

b) proportion who do not pay with cash =P(A)+P(B)=p=0.6+0.2=0.8

mean=np=100*0.8=80

variance =np(1-p)=100*0.8*(1-0.2)=16

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.