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 at least 10 pay in cash?

Question

Quizplus · Accepted Answer

In this question, we are dealing with a binomial distribution because there are only two outcomes (paying in cash or not) for each customer and the probability of success (paying in cash) is constant for all customers.

We can use the binomial probability formula:

P(X≥10) = 1 - P(X<10)

where X is the number of customers who pay in cash, and P(X<10) is the probability that less than 10 customers pay in cash.

P(X<10) = ΣP(X=k) for k=0 to 9

P(X=k) = nCk * p^k * (1-p)^(n-k)

n = 15 (total number of customers)
p = 0.4 (probability of paying in cash)

Using a binomial probability table or calculator, we can find:

P(X<10) = 0.966

Therefore,

P(X≥10) = 1 - P(X<10) = 0.034

The closest answer choice is B, 0.033, which is within rounding error.

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