statistic 3303

Case 2 Instruction (Sales Estimation):

For the coming season, Specialty Toys, Inc., plans to introduce a new

product called Weather Teddy. Specialty’s managers claimed Weather Teddy

gave predictions that were as good as many local TV weather forecasters!

Now, Specialty faces the decision of how many Weather Teddy units to

order from manufacturers for the coming holiday season. Members of the

management team suggested four order quantities of 15,000, 18,000, 24,000,

or 28,000 units. The team asks you for an analysis of the stock-out

probabilities for various order quantities, an estimate of the profit potential,

and to help make an order recommendation.

Specialty expects to sell Weather teddy for $24 based on the unit cost of $20.

If inventory remains after holiday season, Specialty will sell all surplus

inventory for $5 per unit. After reviewing the sales history of similar

products, Specialty’s senior sales forecaster predicted that the demand would

be normally distributed with the mean as 20,000 units and that demand

would be between 5,000 and 35,000 units with a 90% probability.

The managerial report should answer:

1. Use the sales forecaster prediction to calculate the standard deviation for the demand distribution. (20%)

2. Compute the probability of quantity demanded less than 6,000 units. (20%)

3. Compute the probability of a stock-out (i.e. quantity demanded is greater than the order quantity) for each order quantity suggested by

the management team. (20%)

4. One of Specialty’s managers felt strongly that the order quantity should have an 80% chance of meeting quantity demanded (i.e. only a

20% chance of stock-out). What quantity should be ordered under this

policy? (20%)

5. Given the order quantity answered in Question 4, if the quantity demanded in the coming season will be only 20,000 units, then how

much the profit will be earned? (20%)