A catalog 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 waiting time was found to be a random variable best approximated by an exponential distribution with a mean length of waiting time equal to 3 minutes (i.e. the mean number of calls answered in a minute is 1/3). 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

The exponential distribution has the probability density function f(x) = λe^(-λx), where λ = 1/mean. Here, λ = 1/3. We need to find the time t such that P(X > t) = 0.10. This is equivalent to finding t such that 1 - F(t) = 0.10, where F(t) is the cumulative distribution function. Solving 1 - e^(-t/3) = 0.10 gives t ≈ 6.9 minutes.

A Catalog Company That Receives the Majority of Its Orders