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SPRING
2014
SIDDIQUI
10


EN.560.348: Quiz 2 February 11, 2014
INSTRUCTIONS: Show work to receive full credit! Make sure you flip over to check for any
remaining questions.
1. (2 pts) A water pipeline system is made up of three links in a series. The probability of
failure in each link (i.e., the probability that the pipeline link will not be able to deliver
water) is 0.01 in any given year. The condition between the links is statistically
independent. Compute the probability of failure of the pipeline system.
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2. (3 pIs) Of every 100 cars approaching an interstate junction, 60 will go straight, 15 will
make a left turn, and the rest will make a right turn.
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(a) What is the probability that a car approaching the junction will make a turn?
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(b) It is certain that an approaching car will make a turn, what is the probability that it
will be a right turn?
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3. (5
pts)
Three construction companies (designated
A,
Band C) are bidding on ajob. These
companies have equal chances to win the job. From past performance records, if either
Company
A
or
B
wins the job, there is a 0.80 probability that the job will be completed on
time. The corresponding probability for Company C is 0.90.
(a) Not knowing which company will win the job; compute the probability that it will be
completed as scheduled.
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(b) Given that the completion time is delayed, compute the probability that Company A
won the job.

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SPRING
2014
SIDDIQUI
(0
EN.560.348: Quiz 4 February 25,2014
INSTRUCTIONS: Show work to receive full credit! Make sure you flip over to check for any
remaining questions.
Below is the coefficient of variation (COV) formula for your reference:
a
COV
=
15
= 
J1
1. (3 pts) The maximum tensile force in a cable follows a normal probability density
function with a mean = 55 kN and a COY = 0.25. The resistance of the cable is 75 kN
(the resistance is not a random variable). Compute the probability of failure of the cable.
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2. (7 pts) The waiting time
(1)
for a car before it can make a left turn at an intersection is
modeled with the following probability density function:
J
(t)
=
h ( 2  3
t
O)
J(t)
=
0
for 30 :::;
t :::;
60 sec
elsewhere
(a) If
h
is constant, compute h.
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=
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