STAT 3345 – PROBABILITY MODELS FOR
ENGINEERS
SPRING 2010
SAMPLE MIDTERM 1 EXAM
Problem 1
A university librarian produced the following probability distribution of the number
of times a student walks into the library over the period of a semester.
x
0
5
10
15
20
25
30
40
50
75
100
p
(
x
)
.22
.29
.12
.09
.08
.05
.04
.04
.03
.03
.01
(a)
Calculate the mean of
X
.
(b)
Calculate the standard deviation of
X
.
Problem 2
The following data represent the birth weights (in grams) of babies born in 2002
along with the period of gestation.
Birth Weight
Period of Gestation
(in grams)
Preterm
Term
Postterm
Total
Less than 1000
28,247
202
32
28,481
10001999
78,532
10,325
1,051
89,908
20002999
228,064
606,046
39,481
873,591
30003999
135,790
2,293,927
192,566
2,622,283
40005000
8,974
315,821
34,319
359,114
Over 5000
211
4,524
556
5,291
Total
479,818
3,230,845
268,005
3,978,668
(a)
What is the probability that a randomly selected baby born in 2002 was
preterm?
(b)
What is the probability that a randomly selected baby born in 2002 weighted
less than 3000 grams?
1
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(c)
What is the probability that a randomly selected baby born in 2002 weighted
less than 3000 grams or was preterm?
(d)
Are the event the baby born in 2002 weighted less than 3000 grams and the
event the baby was preterm independent?
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