Final Exam
Name
You are required to show your work on every problem in this test
No credit will be given for unsupported answers.
You may use your calculators on this test if you so desire.
Read instructions FULLY before starting a problem.
GOOD LUCK!
Prob. 1 (10 pts) Answer the following questions by writing the
word "true" or the word "false" in the blank precedidng the problem.
a.
The lines y=3x+1 and 3y - 6x = 4 are perpindicular.
b.
If two dice are cast and the numbers are added to form a sample space S, then
S will have equally likely outcomes.
c.
In counting the number of ways to form a committee you would use a permutation.
d.
If A is 
matrix and B is a 
matrix then A+B is
not defined.
e.
If an experiment consists of flipping a coin twice, then 
is a complete and valid random variable
for this experiment.
f. In a binomial experiment each
trial must be dependent on the previous trial.
g. If E and F are events in some
sample space S then 
.
h. If two lines are parallel then
either the system has no solutions or the system has many solutions.
i.If A is a matrix
then 
will be a matrix.
j. If A and B are sets then
.
Prob. 2 (10 pts) A manufacturer makes two models of televisions, one is a 12 inch model and the other is a 15 inch model. Sixty-five percent of all production capacity is allotted to the 12 inch model. Approximately 3 percent of the 12 inch models are defective and approximately 1 percent of the 15 inch models are defective.
a. Find the probability that a television is defective given that it is a 12 inch model.
b. Find the probability that a randomly chosen television is defective.
Prob. 3 (10 pts) Honest Al's Car Parts has found that the automobile batteries it sells have a normally distributed life expectency with a mean of 50 months and a standard deviation of 3 months.
a. What is the probability that one of these batteries will last for at least 56 months?
b. What is the probability that one of these batteries will last for between 46 and 54 months?
c. If Honest Al sells these batteries with a 44 month warranty what percentage of them will be returned for a warranty adjustment?
Prob. 4 (10 pts) It is estimated that one-third of the general population
is blood type 
. If 29 people are chosen at random and X denotes the
random variable "the number of people who are " then find:
a. P(X = 27) =
b. 
c. The mean and the standard deviation of X.
Prob. 5 (10 pts) The table below classifies the English, History, Math and Poly Sci students at t.u. according to their year.
a. Find the probability that a student is in History and a Sophmore.
b. Find the probability that a student is in Math or is a Senior.
c. Find the probability that a student is in English given that the student is a Freshman.
Prob. 6 (10 pts) Three marbles are selected at random without replacement
from a jar containing three white marbles and four blue marbles. Let X denote
the number of blue marbles drawn.
a. Find the probability distribution of X and draw a Histogram
representing this distribution.
b. Find the standard deviation of X.
Prob. 7 (5 pts) Let 
, 
, 
, 
and
.
a. Find 
.
b. Find 
.
c. Find 
.
d. Find 
.
e. Is 
a subset of 
? Why or Why not?
Prob. 8 (10 pts) A survey was conducted to see who plays cards, who plays dominoes and who plays pool. 199 people said they played dominoes, 215 play cards, 207 play pool, 76 play dominoes and pool, 67 play cards and pool, 84 play cards and dominoes, 11 play all three games and 92 play none of these games.
a. How many people play only pool?
b. How many people play only cards OR only dominoes?
c. How many people participated in the study?
Prob. 9 (5 pts) A company is conducting a survey and wishes to classify everyone who responds to the survey according to age, sex, income level, physical fitness and marital status. On the survey each respondent has three choices for age, two for sex, six for income level, four for physical fitness and three for marital status. How many possible classifications are there?
Prob. 10 (6 pts) Exxon corporation sends 17 representatives to a
conference and Standard Oil sends 26 representatives to the same conference.
A steering committee of 7 people is to be chosen from among these
representatives.
a. In how many ways can the committee be chosen if there are no
restrictions?
b. In how many ways can the committe be chosen if exactly two people on the committee must be from Standard Oil?
Prob. 11 (5 pts) Suppose I deal five cards from a well-shuffled 52-card deck, what is the probability of drawing a four of a kind in this hand?
Prob. 12 (6 pts) A refinery processes gasoline and fuel oil. The refining
process demands that at least 3 gallons of gasoline to each gallon of fuel oil
be refined. To meet the demand, at least 4.2 million gallons of fuel oil per
day must be refined. The demand for gasoline is no more than 7.6 million
gallons per day. If the refinery sells gasoline for $0.87 per gallon and fuel
oil for $1.20 per gallon, how many gallons of each product should be
refined each day to maximize revenues?
Set up but DO NOT SOLVE the linear programming problem described above. Write
the initial tableau.
Prob. 13 (10 pts) Let
,
,
and
If possible compute each of the following. (If not possible explain why).
a. 
b. 
c. 
d. 
e.
Prob. 14 (8 pts) Solve the following linear programming problem.
Maximize P= x + 4y subject to
Prob. 15 (7 points) Solve the following system of linear equations.
