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Managerial Report on Application of Business Statistics Presented by P.JASEEM BHAVYA SHAH KARTIK CHOUBEY MOHINI P.BHASKAR

CASE STUDY
SPECIALITY TOYS
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,
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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 projetions.Provide a rationale for your recommendation

Solution
Let X be the demand for the toy. Then X follows normal distribution with mean μ = 20000 and standard deviation σ. Then P(10000 < X < 30000) = 0.95
P((10000-20000)/σ < (X-20000)/σ < (30000-20000)/σ) = 0.95
From tables of areas under the standard normal curve (30000-20000)/σ = 1.96 σ = (30000-20000)/1.96 =10000/1.96 = 5102 1. The demand distribution can be approximated by a normal distribution with mean µ = 20000 and standard deviation σ = 5102.

2. Probability of stock out with an order of K units is P(X > K) = P(Z > (K-20000)/5102), where Z is distributed as standard normal Order (K) | (K-20000)/5102 | P(X > K) | 15000 | -0.98001 | 0.836458876 | 18000 | -0.392 | 0.652472052 | 24000 | 0.784006 | 0.216518215 | 28000 | 1.568013 | 0.058439102 |

3. The projected profit for the different order quantities and scenarios are given in the following
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