Probality Question

Question

On average 1.4 complains through e-mails will be received by TECH-Pro Company in every 48 hours. Please assist the customer service executive to calculate the chances of fewer than 3 complains through emails will be received in 60 minutes.

Answer 1

The key to solving this problem is understanding that we are supposed to use the Poisson distribution.

We are given that there are an average of 1.4 complaints per 48 hours and asked for the probability of less than 3 complaints in 60 minutes.

First, we must calculate the rate. This is 1.4 complaints/48 hours * 60 minutes * 1 hour/60 minutes = 7/240

Then, P(< 3 complaints) = P(2 or less complaints). The Poisson distribution is e^-lambda * lambda^x/x!, where lambda is the rate. Thus, we can substitute 7/240 for lambda and solve

e^-(7/240) * (7/240)^x/x! for x = 0, 1, and 2.

e^-(7/240) * (7/240)^0/0! + e^-(7/240) * (7/240)^1/1! + e^-(7/240) * (7/240)^2/2!

An easier way to solve is to use a package like Excel which provides the cumulative probabilities.

In Excel, poisson.dist(2,7/240,1) = 0.999996 Note that the final 1 in the parentheses tells us that this is cumulative; if the value is 0, we get the probability of exactly 2.