A company that receives most of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product.The length of waiting time was found to be a variable best approximated by an exponential distribution with a mean length of waiting time equal to 2.8 minutes (i.e.the mean number of calls answered in a minute is 1/2.8).What is the probability that a randomly selected caller is placed on hold fewer than 7 minutes?
A)0.0009119
B)0.082085
C)0.917915
D)0.9990881

Question

Quizplus · Accepted Answer

The exponential distribution is given by the formula $P(X < x) = 1 - e^{-\lambda x}$, where $\lambda = \frac{1}{\text{mean}} = \frac{1}{2.8}$. For $x = 7$, $P(X < 7) = 1 - e^{-\frac{7}{2.8}} = 1 - e^{-2.5} \approx 0.917915$.

A Company That Receives Most of Its Orders by Telephone