The purpose of this assignment is to know how to apply normal probability distribution concepts to a real business case. The case study starts under Unit 4. and Unit 4.1 is the continuation.Describe a normal probability distribution that can be used to approximate the demand distribution. Sketch the distribution and show its mean and standard deviation.Compute the probability of a stock-out for the order quantities suggested by members of management team. For the coming season, Specialty plans to introduce a new product called WeatherTeddy. This variation of a talking teddy bear is made by a company in Taiwan. When achild presses Teddy's hand, the bear begins to talk. A built-in barometer selects one of fiveresponses that predict the weather conditions. The responses range from "It looks to be avery nice day! Have fun" to "I think it may rain today. Don't forget your umbrella." Testswith the product show that, even though it is not a perfect weather predictor, its predictionsare surprisingly good. Several of Specialty's managers claimed Teddy gave predictions ofthe weather that were as good as those of many local television weather forecasters.As with other products, Specialty faces the decision of how many Weather Teddy unitsto order for the coming holiday season. Members of the management team suggested orderquantities of 15,000, 18,000, 24,000, or 28,000 units. The wide range of order quantitiessuggested indicates considerable disagreement concerning the market potential. The prod-uct management team asks you for an analysis of the stock-out probabilities for variousorder quantities, an estimate of the profit potential, and help with making an order quantityrecommendation. Specialty expects to sell Weather Teddy for $24 based on a cost of $16per unit. If inventory remains after the holiday season, Specialty will sell all surplus inven-tory for $5 per unit. After reviewing the sales history of similar products, Specialty's seniorsales forecaster predicted an expected demand of 20,000 units with a .95 probability thatdemand would be between 10,000 units and 30,000 units. CASE PROBLEM 1: SPECIALTY TOYSSpecialty Toys, Inc. sells a variety of new and innovative children's toys. Managementlearned that the preholiday season is the best time to introduce a new toy, because manyfamilies use this time to look for new ideas for December holiday gifts. When Specialtydiscovers a new toy with good market potential, it chooses an October market entry date.In order to get toys into its stores by October, Specialty places one-time orders with itsmanufacturers 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 marketplace often increases the demandto high levels and large profits can be realized. However, new toys can also flop, leavingSpecialty stuck with high levels of inventory that must be sold at reduced prices. The mostimportant question the company faces is deciding how many units of a new toy should bepurchased to meet anticipated sales demand. If too few are purchased, sales will be lost; if toomany are purchased, profits will be reduced because of low prices realized in clearance sales.

Expected selling price = $24 Cost = $16 Salvage value = $5

Answered: Describe a normal probability…

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The purpose of this assignment is to know how to apply normal probability distribution concepts to a real business case. The case study starts under Unit 4. and Unit 4.1 is the continuation.

Describe a normal probability distribution that can be used to approximate the demand distribution. Sketch the distribution and show its mean and standard deviation.
Compute the probability of a stock-out for the order quantities suggested by members of management team.

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 those of many local television weather forecasters.
As with other products, 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 15,000, 18,000, 24,000, or 28,000 units. The wide range of order quantities
suggested indicates considerable disagreement concerning the market potential. The prod-
uct management team asks you for an analysis of the stock-out probabilities for various
order quantities, an estimate of the profit potential, and help with making 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 inven-
tory 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 with a .95 probability that
demand would be between 10,000 units and 30,000 units.

CASE PROBLEM 1: 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 into 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 marketplace 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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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