Question

Hello, below is a copy of a homework question. Here they ask the question and then explain how to go about solving it. Could anyone please tell me why ( 0.84162 × 10 = 8.416) was times by ten? i cant find any reason in my notes why this was done. Many Thanks

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A busy café manager has to decide how many cookies to order in for the Tuesday lunch rush. If the manager doesn’t put enough sandwiches out in the display some customers will miss out and the café will lose the profit associated with these sales. On the other hand, if too many cookies are placed in the display, the manager has used and paid for the cookies that were not sold during the day, lowering profit for the day.

A simple way to think about this is to consider how much risk we are willing to take for running out of inventory.

Data Collected by the Manager over previous 6 months shows that

• 50 cookies (average) were sold on a Tuesday. Note the manager purposefully overstocked the cookies during this period in order not to run out, and to determine what the ‘real’ demand was.

What is the acceptable unit rate? To be 80% sure of not running out of cookies on a Tuesday.

SOLUTION

If we assume the probability distribution associated with the sales of the cookies is normal, that if we stocked exactly 50 cookies each Tuesday for the lunch rush, the risk of running out of stock would be 50% since 50% of the time expect demand to be less than 50 cookies and 50% of the time we expect demand to be greater than 50.

To be 80% sure of not stocking out, we need to carry a few more cookies and we can calculate how many extra by using the standard deviation table and formulas found in Microsoft excel that will tell us exactly how many more units to order.

From the “cumulative standard normal distribution” table, we see that we need approximately 0.85 standard deviation of extra cookies to be 80% sure of not stocking out.

A quick way to find the exact number of standard deviations needed for a given probability of stocking out is with the NORMSINV (probability) function in Microsoft Excel (NORMSINV (0.8) = 0.84162).

Given our result from Excel, which is more accurate than what we can get from the tables, the number of extra cookies would be 0.84162 × 10 = 8.416, or 9 cookies (you wouldn’t sell 0.4 of a cookie!).

Answer 1

Paga Na Here you have to compute acceptable unit rate. on an average 50 cookies wee sold on Tuesday. Here we have 801 sure of not a running ou do cookies on a Tuesday That means we have no probleme the 204 times of cookies running out Here we have to finde exact numbea or standard deviation to given probability stocking out so, 5ox o.2 - 10 .so awertige cookies sold Tuesday Henre multiply to 0.84 162 by lo times