Homework Assignment #2
Name: __________________________
All calculations should
be done in Word using Equation Editor and all charts and graphs should be done
in Excel.
1)
In the judicial case of the United States vs. the City of Chicago,
discrimination was charged in a qualifying exam for the position of Fire
Captain. In the table below, Group A was the minority and Group B was the
majority. Use this table to answer questions a) â e)
Passed
Failed
Group A
25
22
Group B
410
156
a) If one of the test subjects
is randomly selected, find the probability of getting someone who passed the
exam.
b) Find the probability
of randomly selecting one of the test subjects and getting someone who is in
Group B or passed.
c) Find the probability
of randomly selecting two different test subjects and finding that they are
both is Group A.
d) Find the probability
of randomly selecting one of the test subjects and getting someone who is in
Group A and passed the exam.
e) Find the probability
of getting someone who passed, given that the selected person is in Group A.
2)
About 17% of the
population has blue eyes. If a person is randomly selected, what is the
probability that he or she does not have blue eyes? If four different people
are randomly selected, what is the probability that they all have blue eyes? Would
it be unusual to randomly select four people and find that they all have blue
eyes? Why or why not?
3)
You are trying to develop a strategy for investing in two difference
stocks. The anticipated annual return for a $1,000 investment in each stock
under four difference economic conditions has the following probability
distribution:
Probability
Economic Condition
Returns Stock A
Returns Stock B
0.15
Recession
-25
-75
0.25
Slow Growth
20
55
0.35
Moderate Growth
100
130
0.25
Fast Growth
150
200
a) Compute the expected
return for Stock A and for Stock B
b) Compute the standard
deviation for Stock A and for Stock B
c) Would you invest in
Stock A or Stock B? Explain.
4)
In South Carolina Palmetto
Cash 6 lottery game, winning the jackpot requires that you select the correct 6
numbers between 1 and 57. How many different ways can those 6 numbers be
selected? What is the probability for winning the jackpot? Is it unusual for
anyone to win the lottery? Explain.
Use Excel to calculate
the first question.
5)
Sun Microsystems has 64% of the market for high-end Unix machine,
with its closest competitor being IBM. Suppose 17 corporations were in the
market to purchase a high-end Unix machine.
Use Excel to answer b) â d) (Hint: Assume a Binomial Distribution)
a) How many Unix machines would Sun Microsystems âexpectâ to sell?
b) What is the probability that exactly 7 corporations purchase a
Unix machine, from Sun Microsystems?
c) What is the probability that less than 11 corporations purchase
a Unix machine from Sun Microsystems?
d) What is the probability that 9 or more corporations purchase a
Unix Machine from Sun Microsystems?
6)
Dutchess County, New
York, has been experiencing a mean of 67 motor vehicle deaths each year.
Use Excel to answer a â
c) (Hint: Assume a Poisson Distribution)
a) Find the mean number of deaths per day.
b) Find the probability that on a given day, there are 2 or more
motor vehicle deaths.
c) Find the probability that on a given day, there are no motor
vehicle deaths.
