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 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)6.9 minutes
D)13.8 minutes

Question

Quizplus · Accepted Answer

For an exponential distribution, the probability density function is given by $f(x) = \frac{1}{\beta}e^{-x/\beta}$, where $\beta$ is the mean. To find the time at which only 10% of customers will continue to hold, we use the cumulative distribution function (CDF), which is $1 - e^{-x/\beta}$. Setting this equal to 0.90 (since 90% have hung up, leaving 10% still holding) and solving for $x$ when $\beta = 3$ gives $x = -3\ln(0.1) \approx 6.9$ minutes.

A Company That Receives Most of Its Orders by Telephone