GOLDEN GATE UNIVERSITY PMBA 305 Module #2

PMBA 305 – Spring ’13
Quantitative Aspects of Decision Making
Module #2: Probability
Concepts and Distributions
Due:

Name

ID#

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 by Runner’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.