After graduation, you take a job with Specialty Toys, Inc, a company that sells a variety of innovative children’s toys. Management has learned the best time to introduce a new toy for the holiday season is in October when many families begin looking for holiday gifts.

Specialty plans to introduce a new product called "Weather Teddy," a talking teddy bear with a built in barometer that predicts weather conditions. When a child presses the bear’s hand, it will respond with one of five possible weather predictions, ranging from "It looks to be a very nice day! Have Fun!" to "I think it may rain today. Don’t forget your umbrella." Product tests show its predictions are about as good as those of many local weather forecasters.

Since you understand statistics, your boss comes to you for help in deciding how many Weather Teddy units to order for the holiday season. She tells you the following facts:

Members of the management team suggest ordering quantities of 15,000, 18,000, or 24,000 units (a unit = one teddy bear). The wide range of order quantities suggested indicates considerable disagreement concerning the market potential of Weather Teddy.

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.

Specialty’s senior forecaster predicts an expected demand (aka mean demand) of 20,000 units, with a 0.90 probability that demand will be between 10,000 units and 30,000 units. He expects the demand will follow a normal distribution.

The senior forecaster predicts a 0.9 probability that the demand will be between 10000 and 30000 units. This implies the middle 90% of the demand distribution is between 10000 and 30000 units. What is the probability the demand will be less than than 30000 units? Use 2 decimal places.

Use the =norm.s.inv(probability)=norm.s.inv(probability) function in Excel to find the zz-score for which the area under the curve to the left of zz is equal to your answer from the previous question. Use 3 decimal places.

We know the mean of the demand distribution is μ=20,000μ=20,000 units, and we have identified the zz-value corresponding to x=30,000x=30,000 units. Now, use those three values and the zz-score formula to solve for the standard deviation σσ of the distribution for demand. Round up to the next whole number.

A stockout occurs when customer orders for a product exceed the amount of inventory kept on hand. Suppose Specialty Toys management decides to order 15,000 units. Using the demand distribution calculated earlier, what is the probability of a stockout? Use 4 decimal places.

What is the probability of a stockout for 18,000 units? Use 4 decimal places.

What is the probability of a stockout for 24,000 units? Use 4 decimal places.

Question

After graduation, you take a job with Specialty Toys, Inc, a company that sells a variety of innovative children’s toys. Management has learned the best time to introduce a new toy for the holiday season is in October when many families begin looking for holiday gifts.

Specialty plans to introduce a new product called "Weather Teddy," a talking teddy bear with a built in barometer that predicts weather conditions. When a child presses the bear’s hand, it will respond with one of five possible weather predictions, ranging from "It looks to be a very nice day! Have Fun!" to "I think it may rain today. Don’t forget your umbrella." Product tests show its predictions are about as good as those of many local weather forecasters.

Since you understand statistics, your boss comes to you for help in deciding how many Weather Teddy units to order for the holiday season. She tells you the following facts:

Members of the management team suggest ordering quantities of 15,000, 18,000, or 24,000 units (a unit = one teddy bear). The wide range of order quantities suggested indicates considerable disagreement concerning the market potential of Weather Teddy.
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.
Specialty’s senior forecaster predicts an expected demand (aka mean demand) of 20,000 units, with a 0.90 probability that demand will be between 10,000 units and 30,000 units. He expects the demand will follow a normal distribution.

The senior forecaster predicts a 0.9 probability that the demand will be between 10000 and 30000 units. This implies the middle 90% of the demand distribution is between 10000 and 30000 units. What is the probability the demand will be less than than 30000 units? Use 2 decimal places.
Use the =norm.s.inv(probability)=norm.s.inv(probability) function in Excel to find the zz-score for which the area under the curve to the left of zz is equal to your answer from the previous question. Use 3 decimal places.
We know the mean of the demand distribution is μ=20,000μ=20,000 units, and we have identified the zz-value corresponding to x=30,000x=30,000 units. Now, use those three values and the zz-score formula to solve for the standard deviation σσ of the distribution for demand. Round up to the next whole number.
A stockout occurs when customer orders for a product exceed the amount of inventory kept on hand. Suppose Specialty Toys management decides to order 15,000 units. Using the demand distribution calculated earlier, what is the probability of a stockout? Use 4 decimal places.
What is the probability of a stockout for 18,000 units? Use 4 decimal places.
What is the probability of a stockout for 24,000 units? Use 4 decimal places.

Accepted Answer

Standard Normal Distribution:
The normal probability distribution is applicable more simply, it is…