A 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 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 proportion of callers is put on hold longer than 2.8 minutes?
A) 0.3679
B) 0.50
C) 0.60810
D) 0.6321

Question

Quizplus · Accepted Answer

The proportion of callers put on hold longer than 2.8 minutes is given by the cumulative distribution function of the exponential distribution, which is given by 1 - e^(-x/mean). In this case, the mean is 2.8 minutes, so the proportion of callers put on hold longer than 2.8 minutes is 1 - e^(-2.8/2.8) = 0.3679.

A Company That Receives the Majority of Its Orders by Telephone