A person must score in the upper 2% of the population on an IQ test to qualify for membership in Mensa. If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, what score must a person have to qualify for Mensa?

A person must score in the upper 2% of the population on an IQ test to qualify for membership in Mensa. If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, what score must a person have to qualify for Mensa?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter9: Decision Making Under Uncertainty

Section9.5: Multistage Decision Problems

Problem 19P

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Based on Babich (1992). Suppose that each week each of 300 families buys a gallon of orange juice from company A, B, or C. Let pA denote the probability that a gallon produced by company A is of unsatisfactory quality, and define pB and pC similarly for companies B and C. If the last gallon of juice purchased by a family is satisfactory, the next week they will purchase a gallon of juice from the same company. If the last gallon of juice purchased by a family is not satisfactory, the family will purchase a gallon from a competitor. Consider a week in which A families have purchased juice A, B families have purchased juice B, and C families have purchased juice C. Assume that families that switch brands during a period are allocated to the remaining brands in a manner that is proportional to the current market shares of the other brands. For example, if a customer switches from brand A, there is probability B/(B + C) that he will switch to brand B and probability C/(B + C) that he will switch to brand C. Suppose that the market is currently divided equally: 10,000 families for each of the three brands. a. After a year, what will the market share for each firm be? Assume pA = 0.10, pB = 0.15, and pC = 0.20. (Hint: You will need to use the RISKBINOMLAL function to see how many people switch from A and then use the RISKBENOMIAL function again to see how many switch from A to B and from A to C. However, if your model requires more RISKBINOMIAL functions than the number allowed in the academic version of @RISK, remember that you can instead use the BENOM.INV (or the old CRITBENOM) function to generate binomially distributed random numbers. This takes the form =BINOM.INV (ntrials, psuccess, RAND()).) b. Suppose a 1% increase in market share is worth 10,000 per week to company A. Company A believes that for a cost of 1 million per year it can cut the percentage of unsatisfactory juice cartons in half. Is this worthwhile? (Use the same values of pA, pB, and pC as in part a.)
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You now have 5000. You will toss a fair coin four times. Before each toss you can bet any amount of your money (including none) on the outcome of the toss. If heads comes up, you win the amount you bet. If tails comes up, you lose the amount you bet. Your goal is to reach 15,000. It turns out that you can maximize your chance of reaching 15,000 by betting either the money you have on hand or 15,000 minus the money you have on hand, whichever is smaller. Use simulation to estimate the probability that you will reach your goal with this betting strategy.
A national survey indicated that 30% of adults conduct their banking online. It also found that 40% are under the age of 50, and that 25% are under the age of 50 and conduct their banking online. A. What is the probability that an individual conducts banking online given that the individual is under the age of 50? B. Are Banking Online and Age independent? Explain.
A metropolitan school system consists of three districts—north, south, and central. The north districtcontains 25% of all students, the south district contains 40%, and the central district contains35%. A minimum-competency test was given to all students; 10% of the north district studentsfailed, 15% of the south district students failed, and 5% of the central district students failed. What is the probability that a student selected at random failed the test?
A salesperson uses three different airlines. The probabilities of switching from one airline to another in consecutive flights are shown below. If the last flight was on Delta, what is the probability that the next was on American? American Delta Southwest American 0.5 0.25 0.25 Delta 0.2 0.6 0.2 Southwest 0.3 0.3 0.4 A 0.5 B 0.2 C 0.25 D 0.6
Suppose the equilibrium price for good quality used cars is $20,000. And the equilibrium price for poor quality used cars is $10,000. Assume a potential used car buyer has imperfect information as to the condition of any given used car. Assume this potential buyer believes the probability a given used car is good quality is .60 and the probability a given used car is low quality is .40. Assume the seller has perfect information on all cars in inventory. What policy or mechanism could solve any informational imbalances and restore the market to an efficient allocation of used cars? a. Third-party provided information on the history of the car (ex: maintenance records, accident records, verified millage and verify repairs). b. Legal remedies and laws restricting fraudulent sales of used cars. c. Obtainablepublications discussing quality, price and possible repairs of all cars --used and new. d. All of the above.
At the beginning of each day, a patient in the hospital is classifed into one of the three conditions: good, fair or critical. At the beginning of the next day, the patient will either still be in the hospital and be in good, fair or critical condition or will be discharged in one of three conditions: improved, unimproved, or dead. The transistion probabilities for this situation are Good Fair Critical Good 0.65 0.20 0.05 Fair 0.50 0.30 0.12 Critical 0.51 0.25 0.20 Improved Unimproved Dead Good 0.06 0.03 0.01 Fair 0.03 0.02 0.03 Critical 0.01 0.01 0.02 For example a patient who begins the day in fair condition has a 12% chance of being in critical condition the next day and a 3%…
A metropolitan school system consists of two districts, east and west. The east district contains 35% of all students, and the west district contains the other 65%. A vocational aptitude test was given to all students; 10% of the east district students failed, and 25% of the west district students failed. Given that a student failed the test, what is the posterior probability that the student came from the east district?
At Tech Innovators Corporation, a study was conducted to assess employees' job satisfaction and their engagement in professional development activities. Out of the 500 employees surveyed: 220 employees reported being satisfied with their jobs. 350 employees were engaged in some form of professional development. 180 employees were both satisfied with their jobs and engaged in professional development. What is the probability that a randomly selected employee from the company is satisfied with their job? Given that an employee is engaged in professional development, what is the probability that they are also satisfied with their job? What is the probability that an employee who is not engaged in professional development is satisfied with their job?
A NY Times best-selling author wants to write a new book as either volume II of her earlier successful book or an autobiography. She believes that by writing the volume II, given her previous success, she will have a 50% chance of placing it with a major publisher where it should ultimately sell about 40,000 copies. However, the worst-case scenario, if she can’t get a major publisher to take it, then she thinks there is 80% chance of placing it with a smaller publisher, with sales of 30,000 copies. On the other hand, if she writes an autobiography, considering the potential interest in her journey as successful writer, she thinks there will be 40% chance of placing it with a major publisher, and it should result in ultimate sales of about 50,000 copies. If she can’t get a major publisher to take it, the worst-case scenario, she thinks there is a 50% chance of placing it with a smaller publisher, with ultimate sales of 35,000 copies. Construct a decision tree to help this author…