# Specialty Toys Case Study

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Specialty Toys Case Study 1. The mean is 20,000 units and there is a 95% probability that demand will be between 10, 000 and 30,000 units. This means there is a .025% chance that the demand will be outside of 10,000 and 30,000. Using the chart, we find that z=-1.96. Using the following calculation, we find: z= x- μ σ -1.96 = 10,000 – 20,000 σ σ=5102 Standard deviation σ = 5,102 μ = 20,000 mean 2. Stock outs were calculated by the four management numbers. Equation is: z = (x – μ)/ σ 15,000: Z = (15,000-20,000)/5102 z = -0.98 Then, reference the cumulative probabilities for standard deviation table in the beginning of the book to identify what -0.98 represents, which is .1635. Since stock outs are any quantity greater than what management suggested, they need to be subtracted from 1. 1 - .1635 = .8365 which = 83.65% Same logic/steps for the rest of the values: 18,000 24,000 28,000 Z = (18,000-20,000)/5102 z=(24,000-20,000)/5102 z=(28,000-20,000)/5102 z = -.39 z=.78 z= 1.57 1 - .3483 = .6517 1 - .7823 = .2177 1 –.9418 = .0582 which = 65.17% which = 21.77% which = 5.82% 3. Projected Profit for management under three scenarios which are 10,000 20,000 and 30,000 units Order | 10,000 units | 20,000 units | 30,000 units | 15000 | 8*10000-11*5000 =\$25000 | 8*15000=\$120000 | 8*15000 = \$120000 | 18000 |