Question

A cell phone salesman works for 8 hours per day. He has kept records of his sales and has observed that he sells 9 Noktel cell phones per working day on average. (this is all the information given.)

The Salesman wants to balance his stock of Noktel cell phones. Excess inventory is expensive but he also wants to avoid running out of Noktel phones. How many Noktel phones must he have in stock tomorrow if he wants to be at least 95% sure he doesn’t run out of stock during the day tomorrow?

Answer 1

We will use Poisson distribution to solve this question because we are given the average sale per working day. (whenever we are given average/rate/arrival-pattern we use poisson distribution)

We have,

Let X: Number of Noktel phones in stock for tomorrow

Then, Noktel phones he must have in stock tomorrow if he wants to be at least 95% sure he doesn’t run out of stock during the day are:

Now, if we check a poisson distribution table, we will find that for

Thus, the salesman must have 14 Noktel phones with him.