Question

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 at least ten pay in cash?

Answer 1

0.6535

Explanation:

Given that during a one-hour period twenty-five customers buy gasoline at this station.

Let X be the no of persons out of these 25 who pay by cash.

X has two outcomes and each trial is independent of other.

Hence X is binomial (n=25, p=0.40)

Required probability

=
`P(X\geq 10)\\=P(10)+P(11)+...+P(25)\\=\Sigma_(10)^(25)  25Cr (0.4)^r (1-0.4)^(25-r)`

=0.6535