Standard Deviation and Probability
A business graduate very much wants to get a job in any one of the top 10 accounting firms. Applying to any of these companies requires a lot of effort and paperwork and is therefore costly. She estimates the cost of applying to each of the 10 companies and the probability of getting a job offer there. These data are tabulated below. The tabulation is in the decreasing order of cost.
1. If the graduate applies to all 10 companies, what is the probability that she will get at least one offer?
2. If she can apply to only one company, base on cost and success probability criteria alone, should she apply to company 5? Why or why not?
3. If she applies to companies 2,5,8, and 9, what is the total cost? What is the probability that she will get at least one offer?
4. If she wants to be at least 75% confident of getting at least one offer, to which companies should she apply to minimize the total cost?
5. If she is willing to spend $1,500, to which companies should she apply to maximize her chances of getting at least one job?
Company 1 2 3 4 5 6 7 8 9 10
Cost $870 $600 $540 $500 $400 $320 $300 $230 $200 $170
Probability 0.38 0.35 0.28 0.20 0.18 0.18 0.17 0.14 0.14 0.08
A manufacturing company regularly consumes a special type of glue purchased from a foreign supplier. Because the supplier is foreign, the time gap between placing an order and receiving the shipment against that order is long and uncertain. This time gap is called “lead time.” From past experience, the materials manager notes that the company’s demand for glue during the uncertain lead time is normally distributed with a mean of 187.6 gallons and a standard deviation of 12.4 gallons. The company follows a policy of placing an order when the glue stock falls to a predetermined value called the “reorder point.” Note that if the reorder point is x gallons and the demand during lead time exceeds x gallons, the glue would go “stock-out” and the production process would have to
1. If the graduate applies to all 10 companies, what is the probability that she will get at least one offer?
2. If she can apply to only one company, base on cost and success probability criteria alone, should she apply to company 5? Why or why not?
3. If she applies to companies 2,5,8, and 9, what is the total cost? What is the probability that she will get at least one offer?
4. If she wants to be at least 75% confident of getting at least one offer, to which companies should she apply to minimize the total cost?
5. If she is willing to spend $1,500, to which companies should she apply to maximize her chances of getting at least one job?
Company 1 2 3 4 5 6 7 8 9 10
Cost $870 $600 $540 $500 $400 $320 $300 $230 $200 $170
Probability 0.38 0.35 0.28 0.20 0.18 0.18 0.17 0.14 0.14 0.08
A manufacturing company regularly consumes a special type of glue purchased from a foreign supplier. Because the supplier is foreign, the time gap between placing an order and receiving the shipment against that order is long and uncertain. This time gap is called “lead time.” From past experience, the materials manager notes that the company’s demand for glue during the uncertain lead time is normally distributed with a mean of 187.6 gallons and a standard deviation of 12.4 gallons. The company follows a policy of placing an order when the glue stock falls to a predetermined value called the “reorder point.” Note that if the reorder point is x gallons and the demand during lead time exceeds x gallons, the glue would go “stock-out” and the production process would have to