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).Find the waiting time at which only 10% of the customers will continue to hold.
A) 2.3 minutes
B) 3.3 minutes
C) 6.9 minutes
D) 13.8 minutes

Question

Quizplus · Accepted Answer

The exponential distribution is defined by the probability density function f(x) = λe^(-λx), where λ is the rate parameter. The mean is 1/λ, so λ = 1/3. To find the waiting time at which only 10% of customers will continue to hold, we need to find the 90th percentile of the distribution. This is given by the formula: -ln(1-p)/λ, where p is the percentile (0.9 for 90%). Plugging in the values, we get -ln(0.1)/(1/3) ≈ 6.9 minutes.

A Company That Receives the Majority of Its Orders by Telephone