David's gasoline station offers 4 cents off per litre 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?
A) 0.541
B) 0.401
C) 0.380
D) 0.562

Question

Quizplus · Accepted Answer

This problem follows a binomial distribution with parameters n = 25 and p = 0.4, where X is the number of customers who pay in cash.

We want to find P(10 < X < 15).

Using a binomial probability table, we can compute:

P(X > 10) = 1 - P(X ≤ 10) = 1 - 0.879 = 0.121

P(X < 15) = P(X ≤ 14) = 0.966

Therefore,

P(10 < X < 15) = P(X < 15) - P(X ≤ 10) = 0.966 - 0.879 = 0.087

So the answer is C) 0.380.

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