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(B)=0.2,and P(C)=0.4. (a) Among the next 100 customers, what are the mean and variance of the number who pay with a debit card? meancustomersvariancecustomers2 Explain your reasoning. 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 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. (b) Answer part (a) for the number among the 100 who dont

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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(B)=0.2,and P(C)=0.4.  (a) Among the next 100 customers, what are the mean and variance of the number who pay with a debit card?  meancustomersvariancecustomers2  Explain your reasoning.  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 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.  (b) Answer part (a) for the number among the 100 who dont

Stella Calderon · Accepted Answer

Step 1   Given that,   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(B)=0.2,and P(C)=0.4.   Reasoning:   Because we are interested in whether or not a debit card was used, we can use the binomial distribution.    Let X= the number of customers who use a debit card.    Here, probability of customers who pay with debit card (or success) is p=0.2   Step 2   (a) Mean and variance of the number of customers who pay with a debit card:   The mean number of customers who pay with a debit card can be calculated as given below:  μ=np  =100×0.2  =20  The variance of the number of customers who pay with a debit card can be calculated as given below:  σ2=np(1−p)  =100×0.2(1−0.2)  =16  Step 3   (b) Mean and variance of the number of customers who dont

Corgnatiui · Accepted Answer

Step 1a) Mean =n×p=100×0.2=20variance =n×p×(1−p)=100×0.2×0.8=16b) P(c′)=1−0.4=0.6mean =100×0.6=60variance =n×p×(1−p)=100×0.6×0.4=24

nick1337 · Accepted Answer

Step 1 Given that customers at a gas station pay with a credit card (A), debit card (B), or cash (C). To find out the mean and variance of the number who pay with a debit card for 100 customers We can sort persons using a debit card or not.  Thus there are two outcomes with p=success for each trial=0.6 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 out of 100 customers Mean=np=60and variance=npq=24 Similarly for no of customers do not pay with cash is binomial with p=0.8 Mean=80and variance=16

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

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