MATH 333:Probability & Statistics. Exam 1 (Spring 2002) Score ··
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February 27, 2002 NJIT
Instructors : S. Balaji,
M. C. Bhattacharjee, S.
Dhar, H. Fanik N. Moheb
è Must show all work to receive full credit.
I pledge my honor that I have
abided by the Honor System. ___________________
(Signature)
1. Consider the following
states from the east coast with their corresponding percentage of the adult
population who were obese (1998 data).
East Coast States 
CT 
DE 
MA 
MD 
NJ 
NY 
PA 
VA 
W.Va 
Percent (%) obese 
15.9 
16.2 
14.2 
19.0 
13.8 
14.7 
20.1 
17.5 
24.2 
(i) (6 points) What
are the average and median percentage obesity values among adults over the specified east coast states?
(ii) (7 points) What is the value of
sample standard deviation?
(iii) (7 points) Use the method of box plot
to check for any (mild or, extreme) outliers in the
data. Show work.
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2.
In a shipment of 15 transistors;
6 are good (no defects), 6 have minor defects, while the remaining
transistors in the shipment have major defects. Suppose we choose 4 transistors
at random, from this shipment, without replacement.
Find the probability that:
(a) (3 points) none is good,
(b)
(5 points) at least one is good,
(c)
(3 points) exactly 2 are good,
(d)
(6 points) one is good, one has minor defect and 2 have major defects.
3. (15 points) The Center for Disease
Control has determined that 90% of all persons who are given a vaccine, will
develop immunity. If eight people are independently given this vaccine, find
the probability that:
a)
(5 points) none will develop immunity,
b)
(7 points) at least two will develop immunity.
c)
(5 points) all will develop immunity.
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4. Engineers in charge of maintaining a nuclear power
plant must check for corrosion inside the pipes that are part of the cooling
systems. The inside condition of the pipes cannot be observed directly but a
test can give an indication of possible corrosion. The test has probability 0.9
of detecting corrosion if internal corrosion is present, and a probability 0.05
of falsely indicating corrosion when no internal corrosion is present. Suppose
the probability that any section of pipe has internal corrosion is 0.1.
a) (6 points) Determine the probability that the test
indicates presence of internal corrosion.
b)
(8 points) Determine the probability that a section of pipe has internal
corrosion, given that the test indicates its presence.
5. Six teams compete for the Gold, Silver
and Bronze medals, which correspond to the first, second and third places
respectively, in the final round of Figure Skating at the Winter Olympics. An
outcome lists the three winning teams along with which medal they won.
a) (6
points) How many different
outcomes are there ?
b) (8 points) If
U.S. has three teams among the six competing in the final round; what is
the probability that U.S. wins all three medals ?
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6.
The number of traffic accidents in a certain town during any week is a
random variable with the following
probability distribution:
Number
of accidents 
0 
1 
2 
3 
Probability

0.3 
? 
0.3 
0.15 
a) (2 points) What is
the probability of exactly one accident in a week ?
b) (3 points) Find the probability of
having at least two accidents in a week.
c) (8
points) Find the mean and variance of the number of accidents.
c) (5 points) If the
number of accidents in different weeks are independent, what is the probability
that there are no accidents in a consecutive 3 week period ?
END