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 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

Since the waiting time is best approximated by an exponential distribution, we can use the formula P(X > x) = e^(-λx), where λ is the rate parameter equal to the mean waiting time (1/λ = 2.8). 
Thus, P(X > 2.8) = e^(-2.8/2.8) = e^(-1) = 0.3679. 
Therefore, the proportion of callers put on hold longer than 2.8 minutes is 0.3679 or 36.79%.

A Company That Receives Most of Its Orders by Telephone