PMBA 305 – Spring ’13

Quantitative Aspects of Decision Making

Module #2: Probability Concepts and Distributions

Due: February 8, 2013

Professional Master of Business Administration Program

The Ageno School of Business

GOLDEN GATE UNIVERSITY

[1] a) In how many ways can six banquet speakers be seated along one side of the head table?

b)Gym lockers are to be numbered from 1 to 99 using individual metal number plates to be placed on each locker. How many 7’s are needed?

c)In how many ways can a hostess place six name placecards around a round table?

d)In how many ways can five different keys be put in a flat leather key case?

e)In how many ways can five different keys be put on a key ring?

f)You have one apple, one orange, one banana, and one grapefruit. How many different ways can you hand out all the fruit to 5 people, if no person gets more than one kind of fruit?

g)If I am to paint our house by myself, it will take 4 days to complete painting the house. If my wife is to paint the house alone, it will take 6 days to complete her work. How many days will it take to paint our house if we decide to work together (without fight)?

h)Joey and Ross along with 4 other best friends go to see a movie. They find a row of 6 seats, but Joey and Ross don’t want to sit next each other. How many different seating arrangements are possible if Joey and Ross don’t want to sit next each other?

[2] A particular airline has 10:00 a.m. flights from San Francisco to New York, Atlanta, and Miami. The probabilities that each flight is full are 0.60, 0.40, and 0.50 respectively, and each flight is independent one another.

a)What is the probability that all flights are full?

b)What is the probability that only the New York flight is full?

c)What is the probability that exactly one flight is full?

[3]There is a saying about initial public offerings (IPOs) of stock: “If you want it, you can’t get it; if you can get it, you don’t want it.” This is because it is often difficult for the general public to obtain shares initially when a “hot” new company first goes on sale. Instead, most of us have to wait until it starts trading on the open market, often at a substantially higher price. Suppose that, given that you can obtain shares at the initial offering, the probability of the stock performing well is 0.35. However, given that you are unable to initially purchase shares, the probability of the stock performing well is 0.80. Overall, assume that you can obtain shares in about 15% of IPOs.

a)Find the probability that both you are able to purchase the stock at the initial offering and the stock performs well.

b)Find the probability that the stock turned out not to perform well if you were unable to obtain such shares.

c)How much access to successful IPOs do you have, i.e. what is the probability that you can buy successful IOPs?

d)What percentage of the time, over the long run, will you be pleased with the outcome?

[4] In a past presidential election, the actual voter turnout was 61%. In a survey, 1002 subjects were asked if they voted in the presidential election.

a)Find the mean and standard deviation for the number of actual voters in groups of 1002.

b)In the survey of 1002 people, 701 said that they voted in the last presidential election (based on data from ICR Research Group). Is this result consistent with the actual voter turnout, or is this result unlikely to occur with an actual voter turnout of 61%? Why or why not?

c)Based on these results, does it appear that accurate voting results can be obtained by asking voters how they acted?

[5] As reported byRunner’s Worldmagazine, the times of the finishers in the New York City 10-km run are normally distributed with a mean of 61 minutes and a standard deviation of 9 minutes.

a)What is the chance that finishers complete the run with the times between 50 and 70 minutes?

b)What is the chance that finishers complete the run with the times more than 75 minutes?

c)How fast do finishers have to complete the run among the top 5% finishers?

[6] In a clinical trial of Lipitor, a common drug used to lower cholesterol, 863 patients were given a treatment of 10-mg Atorvastatin tablets. Among them, 19 patients experienced flu symptoms and 844 patients did not (based on data from Pfizer, Inc.).

a)Estimate the probability that a patient taking the drug will experience flu symptoms.

b)Is this unusual for a patient taking the drug to experience flu symptoms? Explain.

c)If you know that the probability of flu symptoms for a person not receiving any treatment is 0.019, what is the probability that there are 19 who experience flu symptoms among 863 patients? Explain.

d)Is this unusual to find that among 863 patients, there are 19 who experience flu symptoms in c)? Explain.