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 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 4.5 minutes will hang up before placing an order?
A) 0.22313
B) 0.51342
C) 0.48658
D) 0.77687

Question

Quizplus · Accepted Answer

The proportion of customers having to hold more than 4.5 minutes will hang up before placing an order is given by the cumulative distribution function of the exponential distribution at 4.5 minutes. The cumulative distribution function of the exponential distribution is given by F(x) = 1 - e^(-x/mean). Substituting the given values, we get F(4.5) = 1 - e^(-4.5/3) = 0.22313.

A Catalog Company That Receives the Majority of Its Orders