PAM 2100
INSTRUCTOR: SALAM ABDUS
SAMPLE FINAL QUESTIONS
In total, there will be 10 problems and 15 multiple choice questions in the final.
Out of the 10 problems, at least 6 problems will be from the material covered after the
second prelim, and at most 4 problems will be from the material covered in the first and the
second prelim.
The 10 problems will be worth 70 points and the 15 multiple choice questions will be worth
30 points.
In what follows, I have given some sample problems and sample multiple choice questions
from the materials covered after the second prelim. In addition to these problems, you
should also look at problem sets #6 to #8, and the problems we have solved during the
lectures.
For sample problems and sample multiple choice questions from the materials covered in
the first and second prelim, look at the previous problem sets, multiple choice questions
which we solved in class, and the answer keys to the two prelims.
Problem 1
Jen and Elise are playing in the club bowling tournament.
Their scores vary as they play
repeatedly.
Jen’s score X has the N(200, 10) distribution, and Elise’s score Y has the N(196, 7)
distribution.
Their scores are independent.
a) What is the mean of (XY)?
What is the standard deviation of (XY)?
Round your answers to
four decimal places if necessary.
4
196
200
=

=

=

Y
X
Y
X
μ
μ
μ
2066
.
12
)
7
(
)
10
(
2
2
2
2
2
=
+
=
+
=
=


Y
X
Y
X
Y
X
σ
σ
σ
σ
b) What is the probability that Jen will score
at least one point higher
than Elise?
Use your final
answers from part a.
Round your z score to two decimal places and then use Table A. Round
your final answer to four decimal places if necessary.
We need to look at the distribution of XY. We need to find out the probability that the value of
this random variable is greater than or equal to one. We know the mean and the standard
deviation of this random variable from (a).
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 Spring '08
 ABDUS,S.
 Statistics, Normal Distribution, Standard Deviation, Statistical hypothesis testing, decimal places

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