A catalogue 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 2.8 minutes.
-What is the probability that a randomly selected caller is placed on hold fewer than 7 minutes?
A) 0.9990881
B) 0.917915
C) 0.0009119
D) 0.082085

Question

Quizplus · Accepted Answer

To solve the problem, we need to use the cumulative distribution function (CDF) of the exponential distribution, which is:

F(x) = 1 - e^(-λx)

where λ is the rate parameter, which is equal to 1/mean for the exponential distribution.

In this case, we have mean = 2.8 minutes, so λ = 1/2.8 = 0.3571 (rounded to 4 decimal places).

Now we can calculate the probability that a randomly selected caller is placed on hold for less than 7 minutes:

P(X < 7) = F(7) = 1 - e^(-0.3571 * 7) = 0.917915 (rounded to 6 decimal places)

Therefore, the answer is B. The probability that a randomly selected caller is placed on hold fewer than 7 minutes is 0.917915.

A Catalogue Company That Receives the Majority of Its Orders