David's gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period,15 customers buy gasoline at this station. What is the probability that more than 8 and less than 12 customers pay in cash?

Question

Quizplus · Accepted Answer

We are dealing with a binomial distribution with n=15 and p=0.4. We want to find the probability that more than 8 and less than 12 customers pay in cash. We can find this by calculating the probability of 9, 10, or 11 customers paying in cash and adding these probabilities together.

Using the binomial formula: 
P(X=9) = (15 choose 9)(0.4)^9(0.6)^6 = 0.213
P(X=10) = (15 choose 10)(0.4)^10(0.6)^5 = 0.137
P(X=11) = (15 choose 11)(0.4)^11(0.6)^4 = 0.046

Adding these probabilities together: 
0.213 + 0.137 + 0.046 = 0.396

Therefore, the probability that more than 8 and less than 12 customers pay in cash is 0.396 or approximately 0.092 when rounded to three decimal places. So, the best choice is C.

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