STATISTICS FOR BUSINESS
LIST OF READING MATERIALS
1. Job Applications
2. Managing Risk
3. Cutcraft Cutlery Corporation
4. Compensation for Faculty Members
5. Airline Satisfaction Survey
6. The Avocado
7. The Mountain States Potato Company
8. Edgartown Fisheries
9. Monitor Systems
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, based 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 that total cost? (This is trial-and-error problem.) 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? (This is a trial-and-error problem.) 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 
Famous golfer Lee Trevino liked to define risk as betting $20 on 18 holes of golf with three guys you don’t know when you only have $2 in your pocket. Investments can differ widely in their amount of inherent risk. Savings deposits at a bank contain very little risk if they are insured by FDIC. Treasury bills offer a narrow range of potential risk. Small-company common stocks typically offer a large range of possible returns, from negative to positive, and so involve much more risk.
Financial advisors like to classify their investors according to their preference or aversion to risk. A risk-taker prefers to gamble and may accept a low rate of return in exchange for a chance at a large return. Risk-neutral investors are indifferent with respect to investment risk. Finally, risk-averse investors prefer to “leave their money under the mattress.” They don’t like risk and demand a high rate of return for any risk undertaken. When an investment has an uncertain return, it can often be described using a discrete random variable. For example, based on past experience, the return for investment A is described according to the following probability distribution: X = Return for Investment A
$1000 with probability .3
$500 with probability .1
$200 with probability .1
$100 with probability .2
$0 with probability .1
- $100 with probability .2
The mean of this random variable, called the expected return, is equal to (-100)(.2) + (0)(.1) + (100)(.2) + (200)(.1) + (500)(.1) + (1000)(.3) = $370 However, if you were to examine the return on this investment, you would observe considerable variation: that is, this investment contains a great deal of risk. This can be measured using the standard deviation of X. The variance of X is equal to (-100)2(.2) + (0)2(.1) + (100)2(.2) + (200)2(.1) + (500)2(.1) + (1000)2(.3) – (370)2 = 196,100 and the standard deviation is 196,100 = $442.8.
The returns for three investments are illustrated in the Figure given at the end of the case. Investment A, the one just described, has the largest expected return but also the largest amount of risk. Investment B has a smaller expected return than A and also involves less risk. Investment C has the smallest expected return and the least risk. Investment A is characteristic of common stock returns. B resembles long-term corporate bonds, and C is like...
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