Suppose Martin is a very talented used-car salesman. Whenever Martin talks to a

Question

Suppose Martin is a very talented used-car salesman. Whenever Martin talks to a new customer, there is a 70% chance that he convinces the customer to purchase one of his used cars. Brian, Martin's boss, is envious that Martin sells many more cars than he does. Because of his jealousy, Brian institutes a new rule that Martin is only allowed to talk to 45 customers per day. Thus, Martin continues to work each day until he speaks to 45 customers, at which point Brian sends him home. Let represent the number of used cars that Martin sells on a given day.

What are the mean, , and variance, 2, of ? Please round your answers to the nearest two decimal places.

Explanation / Answer

Let X be the number of used cars that Martin sells on a given day, with success provabproba p = 0.7 and number of independent trial n = 45

Here X follows Binomial distribution with parameters n = 45 and p = 0.7

Mean of Binomial Variable = np = 45*0.7 = 31.50

Variance = np(1-p) = 45*0.7*0.3 = 9.45

Thus Martin sell the used cars on a given day with mean 31.50 and variance 9.45.

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