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 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 ).What is the probability that a randomly selected caller is placed on hold fewer than 7 minutes?
A)0.0009119
B)0.082085
C)0.917915
D)0.9990881

Question

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 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  ).What is the probability that a randomly selected caller is placed on hold fewer than 7 minutes?
A)0.0009119 
B)0.082085 
C)0.917915 
D)0.9990881

Quizplus · Accepted Answer

The rate parameter for the exponential distribution can be calculated as follows:
rate parameter = 1 / (mean length of waiting time) = 1 / 2.8 = 0.3571

To find the probability that a randomly selected caller is placed on hold fewer than 7 minutes, we need to calculate the cumulative distribution function (CDF) of the exponential distribution at x = 7:

P(X < 7) = 1 - e^(-0.3571 * 7) = 0.917915

Therefore, the probability that a randomly selected caller is placed on hold fewer than 7 minutes is 0.917915, which is option C.

A Catalog Company That Receives the Majority of Its Orders