If the average number of customers served per hour is five,then the probability that the service exceeds 21 minutes for any customer is ______.
A)74.1%
B)54.9%
C)36.8%
D)17.4%

Question

Quizplus · Accepted Answer

We know that on average, 5 customers are served per hour. Therefore, the time taken to serve one customer follows the exponential distribution with parameter lambda=1/5 (since the average service rate is the inverse of the parameter).

The probability that the service time for any one customer exceeds 21 minutes (or 0.35 hours) is given by the cumulative distribution function of the exponential distribution:

P(X > 0.35) = 1 - F(0.35) = 1 - (1 - e^(-lambda*t)) = e^(-lambda*t) = e^(-1/5*0.35) = 0.174 = 17.4%

Therefore, the answer is choice D.

If the Average Number of Customers Served Per Hour Is