Case study 4 covers Chapter 7. You will learn how to apply and calculate one of the important continuous probability distributions we learned in Chapter 7 in Excel. You should use the proper Excel function to calculate the desired probabilities.
Ch. 7-Case Problem-Specialty Toys
Specialty Toys, Inc., sells a variety of new and innovative children’s toys. Management learned that the
preholiday season is the best time to introduce a new toy, because many families use this time to look for
new ideas for December holiday gifts. When Specialty discovers a new toy with good market potential, it
chooses an October market entry date. In order to get toys in its stores by October, Specialty places one-
time orders with its manufacturers in June or July of each year. Demand for children’s toys can be highly
volatile. If a new toy catches on, a sense of shortage in the market place often increases the demand to
high levels and large profits can be realized. However, new toys can also flop, leaving Specialty stuck with
high levels of inventory that must be sold at reduced prices. The most important question the company
faces is deciding how many units of a new toy should be purchased to meet anticipated sales demand. If
too few are purchased, sales will be lost; if too many are purchased, profits will be reduced because of
low prices realized in clearance sales. For the coming season, Specialty plans to introduce a new product
called Weather Teddy. This variation of a talking teddy bear is made by a company in Taiwan. When a
child presses Teddy’s hand, the bear begins to talk. A built-in barometer selects one of five responses that
predict the weather conditions. The responses range from “It looks to be a very nice day! Have fun.” to “I
think it may rain today. Don’t forget your umbrella.” Tests with the product show that, even though it is
not a perfect weather predictor, its predictions are surprisingly good. Several of Specialty’s managers
claimed Teddy gave predictions of the weather that were as good as many local television weather
forecasters. As usual, Specialty faces the decision of how many Weather Teddy units to order for the
coming holiday season. Members of the management team suggested order quantities of 18,000 or
24,000 units. The product management 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 quantity
recommendation. Specialty expects to sell Weather Teddy for $24 based on a cost of $16 per unit. If
inventory remains after the 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 an expected
demand of 20,000 units (mean) with a 0.95 probability that demand would be between 10,000 units and
30,000 units.
Prepare a managerial report that addresses the following issues and recommends an order quantity for
the Weather Teddy product.
1. Use the sales forecaster’s prediction to describe a normal probability distribution that can be
used to approximate the demand distribution. Show the mean and standard deviation of the
distribution.
2. Compute the probability of a stock-out for the order quantities suggested by members of the
management team.
3. Compute the projected profit for the order quantities suggested by the management team
under three scenarios: worst case in which sales = 10 000 units, most likely case in which sales =
20000 units, and best case in which sales = 30 000 units.
4. One of Specialty’s managers felt that the profit potential was so great that the order quantity should have a 70% chance of meeting demand and only a 30% chance of any stock-outs. What
quantity would be ordered under this policy, and what is the projected profit under the three
sales scenarios?
5. Present your findings.
