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QSO 530 Applied Statistics for Managers Class 4: Discrete Distributions Homework Assignment #4 Notes: This homework is to be done individually. Do...

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QSO 530 Applied Statistics for Managers Class 4: Discrete Distributions Homework Assignment #4 Notes: 1. This homework is to be done individually. 2. Word-process your assignment within this template. Do not create a new file. 3. If you notice any errors in this homework assignment, send an email to [email protected] . Assignment Problem 1 (To be done manually using a Calculator) Radio Shack stocks four alarm clock radios. If it has fewer than four clock radios available at the end of a week the store restocks the item to bring the in-stock level up to four. If weekly demand is greater than the four units in stock the store loses the sale. The radio sells for \$25 and costs the store \$15. The Radio Shack manager estimates that the probability distribution of weekly demand for the radio is as follows: x (Weekly Demand) P (X) 0 0.05 1 0.05 2 0.10 3 0.20 4 0.40 5 0.10 6 0.05 7 0.05 (a) What is the expected weekly demand for the alarm clock radio? Show all calculations including the formulas used. x (Weekly Demand) P (X) Expected W demand 0 0.05 0*0.05 = 0 1 0.05 1*0.05 = 0.05 2 0.1 2*0.1 = 0.2 3 0.2 3*0.2 = 0.6 4 0.4 4*0.4 = 1.6 5 0.1 5*0.1 = 0.5 6 0.05 6*0.05 = 0.3 7 0.05 7*0.05 = 0.35 E(x) = E(x) = 0 + 0.05 + 0.2 + 0.6 + 1.6 + 0.5 + 0.3 + 0.35
E(x) = 3.6 (b) What is the probability that weekly demand will be greater than the number of available radios? Show all calculations including the formulas used. The probability will be zero. (c) What is the expected weekly profit from the sale of the alarm clock radio? (Remember: There are only four clock radios available in any week to meet demand.) Show all calculations including the formulas used. Cost = \$15 , Sales = \$25 Profit = Sales - Cost Profit = 25 – 15 = 10 Expected Weekly Profit = E(x) * profit 4*10= \$40 per week (d) On average, how much profit is lost each week because the radio is not available when demanded? Show all calculations including the formulas used. Assignment Problem 2 (Use Excel) Pfizer Inc. is the manufacturer of Revolution (Selamectin), a topical parasiticide used for the treatment, control, and prevention of flea infestation, heartworm, and ear mites for dogs and cats. One of its selling points is that it provides protection for an entire month. Such claims are made on the basis of research and statistical studies. The file entitled Fleafree contains data similar to those obtained in Pfizer's research. It presents the number of days Revolution could remain effective when applied to mature cats. Excel Work Develop a frequency distribution for the number of days variable using Excel. Use the number of days between the minimum and maximum values for the bins. There is no need to group the number of days into classes. Note: Follow all the steps given in the Week 2 Excel tutorial from slides 4 to 11 to develop the distribution. Copy and paste the Excel distribution in the space below. Min 25 Max 33 Number of Freque
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