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 twenty-five customers buy gasoline at this station.
-What is the probability that more than ten and less than fifteen customers pay in cash?

Question

Quizplus · Accepted Answer

This problem can be solved using the binomial probability formula:
P(x) = nCx * p^x * (1-p)^(n-x)
where n is the number of trials, p is the probability of success, x is the number of successes, and nCx is the number of combinations of n things taken x at a time.

In this case, n = 25, p = 0.4, and we want to find the probability that 10 < x < 15. We can find this by calculating the probability of each possible value of x from 11 to 14 and adding them up:
P(11) = 25C11 * 0.4^11 * 0.6^14 = 0.232
P(12) = 25C12 * 0.4^12 * 0.6^13 = 0.295
P(13) = 25C13 * 0.4^13 * 0.6^12 = 0.277
P(14) = 25C14 * 0.4^14 * 0.6^11 = 0.159

Therefore, the probability of having more than 10 and less than 15 customers paying in cash is:

P(11 to 14) = P(11) + P(12) + P(13) + P(14) = 0.232 + 0.295 + 0.277 + 0.159 = 0.380

So the answer is (C).

David's Gasoline Station Offers 4 Cents Off Per Gallon If