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 time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3 minutes. Find the waiting time at which only 10% of the customers will continue to hold.
A) 2.3 minutes
B) 6.9 minutes
C) 3.3 minutes
D) 13.8 minutes

Question

Quizplus · Accepted Answer

The exponential distribution has a mean of 1/λ, so λ = 1/3. To find the time at which only 10% of customers continue to hold, we use the formula for the cumulative distribution function: P(X > x) = e^(-λx). Setting P(X > x) = 0.10 and solving for x gives x ≈ 6.9 minutes.

A Catalog Company That Receives the Majority of Its Orders