A manager wants to determine how many copies of a particular magazine that he should purchase each week. A study of historical data shows that demand is normally distributed with a mean = 11.73 and a standard deviation of 4.74. The manager purchases the magazines for 25 cents and can salvage unsold copies for 10 cents. The price of the magazine that he charges to the customer is 75 cents a copy.
- What is the critical ratio?
- Using the normal tables, what is the standardized z value associated with the critical ratio calculated above?
- How many magazines should the manager order?
Suppose the manager has historical data for the last 52 weeks showing the weekly demand for the magazine. The empirical probability associated with each of the order quantities is give below.
| Q | Frequency | F(Q) | Q | Frequency | F(Q) |
| 0 | 1 | .192 | 12 | 4 | .5769 |
| 1 | 0 | .192 | 13 | 1 | .5962 |
| 2 | 0 | .192 | 14 | 5 | .6923 |
| 3 | 0 | .192 | 15 | 5 | .7885 |
| 4 | 3 | .0769 | 16 | 1 | .8077 |
| 5 | 1 | .0962 | 17 | 3 | .8654 |
| 6 | 2 | .1346 | 18 | 3 | .9231 |
| 7 | 2 | .1731 | 19 | 3 | .9808 |
| 8 | 4 | .2500 | 20 | 0 | .9808 |
| 9 | 6 | .36654 | 21 | 0 | .9808 |
| 10 | 2 | .4038 | 22 | 1 | 1.0000 |
| 11 | 5 | .5000 |
- Calculate the new order quantity for the empirical data given.
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