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

Julia White

Julia White

Answered question

2021-12-18

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

Answer & Explanation

Stella Calderon

Stella Calderon

Beginner2021-12-19Added 35 answers

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(1p)
=100×0.2(10.2)
=16
Step 3
(b) Mean and variance of the number of customers who dont
Corgnatiui

Corgnatiui

Beginner2021-12-20Added 35 answers

Step 1
a) Mean =n×p
=100×0.2=20
variance =n×p×(1p)
=100×0.2×0.8=16
b) P(c)=10.4=0.6
mean =100×0.6=60
variance =n×p×(1p)
=100×0.6×0.4=24
nick1337

nick1337

Expert2021-12-28Added 777 answers

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

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