Problem
A manager of a local grocery store wants to anticipate the sales of Pepsi-Cola for the following month, so that she can prepare enough inventory to meet the demand. She predicts that the demand for the Pepsi-Cola will follow a normal distribution, and the average monthly demand will be 400 with standard deviation of 25.
i. How many Pepsi-Cola should be ordered to satisfy a 98% expected fill rate?
ii. What is the quantity that should be ordered to achieve a 98% in-stock probability?
iii. Even though the percentages for the expected fill rate and in-stock probability are the same, the order quantities differ. In a few sentences, explain the reason behind this difference (i.e., do your answers above-2a and 2b-make sense? which one is greater and why? etc.).