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 3 minutes (i.e.the mean number of calls answered in a
Minute is 1/3).What proportion of customers having to hold more than 4.5 minutes will hang up
Before placing an order?
A) 0.22313
B) 0.48658
C) 0.51342
D) 0.77687

Question

Quizplus · Accepted Answer

The proportion of customers having to hold more than 4.5 minutes is given by the cumulative distribution function of the exponential distribution:P(X > 4.5) = 1 - P(X <= 4.5) = 1 - (1 - e^(-4.5/3)) = e^(-4.5/3) = 0.22313Therefore, the proportion of customers who will hang up before placing an order is 0.22313.

A Company That Receives the Majority of Its Orders by Telephone