A catalogue company that receives the majority 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 time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3 minutes.
-What proportion of customers having to hold more than 1.5 minutes will hang up before placing an order?
A) 0.60653
B) 0.13534
C) 0.39347
D) 0.86466

Question

Quizplus · Accepted Answer

The exponential distribution is given by the formula $P(X > x) = e^{-\lambda x}$, where $\lambda = \frac{1}{\text{mean}} = \frac{1}{3}$ for this problem. For customers waiting more than 1.5 minutes, we calculate $P(X > 1.5) = e^{-\frac{1}{3} \times 1.5} = e^{-0.5} \approx 0.60653$.

A Catalogue Company That Receives the Majority of Its Orders