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.
-Find the waiting time at which only 10% of the customers will continue to hold.
A) 2.3 minutes.
B) 3.3 minutes.
C) 13.8 minutes.
D) 6.9 minutes.

Question

Quizplus · Accepted Answer

The exponential distribution is given by the formula $P(X > x) = e^{-x/\mu}$, where $\mu$ is the mean. To find the time at which only 10% of customers will continue to hold, we set $P(X > x) = 0.1$. Solving for $x$ gives $x = -\mu \ln(0.1)$. Substituting $\mu = 3$ minutes, we get $x = -3 \ln(0.1) \approx 6.9$ minutes.

A Catalogue Company That Receives the Majority of Its Orders