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 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.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 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 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 with a .95 probability that demand would be between 10,000 units and 30,000 units.Managerial ReportPrepare 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. Sketch the distribution and show its mean and standard deviation.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 = 10,000units, most likely case in which sales = 20,000units, and best case in which sales = 30,000units.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. Provide your own recommendation for an order quantity and note the associated profit projections. Provide a rationale for your recommendation.

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You manage Human Relations for your company. One of your sales managers has retired, leaving an opening. You are considering two different employees for the position. Both are highly qualified so you have decided to evaluate their sales performance for the past year. The data showing a sample of their respective sales performance is in the Excel worksheet.1. Annual sales data is provided for a sample of 50 employees.Determine the range of values in which you would expect to find the average weekly sales for the entire sales force in your company 90% of the timeWhat is the impact of increasing the confidence level to 95%?*What is the impact of increasing the sample size to 150, assuming the same mean and standard deviation, but allowing the confidence level to remain at 90%?*2. You want to determine whether there is a statistically different average weekly sales between Sales Rep A and Sales Rep B.Create Null and Alternative Hypothesis statements that would allow you to determine whether their sales performance is statistically different or not.Based on your hypothesis statements, provide an example of a Type I and a Type II error, respectively.Using a significance level of .05, conduct a t-test of independent samples when the standard deviation of the population is unknown to compare the average weekly sales of the two candidates. (NOTE: YOU CAN DO THIS VERY QUICKLY IN EXCEL USING THE DATA ANALYSIS TOOLPAK!)What is the p-value? Based on the p-value, is there a statistically significant difference between the two reps being considered for the manager's position? Explain your reasoning.Who would you recommend to be promoted to Sales Manager - Rep A or Rep B? Why?All Sales Representatives are expected to meet an average weekly sales quota of $4500.Create Null and Alternative Hypothesis statements that would allow you to determine whether the weekly sales of the individual you have decided to promote in #4 (Rep A or Rep B) exceeds the company quota.Based on your hypothesis statements, provide an example of a Type I and a Type II error, respectively.Using a significance level of .05, conduct a one sample mean hypothesis test to determine whether the performance of your chosen candidate exceeds the quota by a statistically significant amount?What is the p-value?Based on the p-value, what is your conclusion? SAMPLE - WEEKLY SALES SAMPLE OF WEEKLY SALES FOR REP A AND B # Sales Rep Weekly Sales $ Week # Weekly Sales - A Weekly Sales - B 1 1228 1 4657 5839 2 7374 2 6133 2602 3 1055 3 3438 2830 4 1859 4 7394 4763 5 3938 5 4327 3740 6 1692 6 2552 1315 7 569 7 7063 1599 8 4059 8 7844 1629 9 3689 9 6898 2416 10 607 10 4003 2107 11 1370 11 6884 4237 12 3735 12 4007 6322 13 3305 13 7214 2710 14 7228 14 2358 5890 15 6279 15 7745 5119 16 1671 16 1337 5184 17 5708 17 1052 3439 18 2569 18 6056 4828 19 4163 19 1495 3667 20 1519 20 3530 2518 21 7734 21 4749 6073 22 784 22 3833 5566 23 6766 23 7869 4555 24 7261 24 4541 5867 25 5034 25 6882 6039 26 7115 26 3868 1032 27 6291 27 5934 4834 28 6287 28 4447 3687 29 2080 29 5504 2214 30 7621 30 5554 4659 31 1047 32 6517 33 5172 34 3876 35 5429 36 4538 37 3786 38 2510 39 4863 40 7246 41 1175 42 641 43 4269 44 7034 45 3406 46 2256 47 3182 48 5178 49 4428 50 1189