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ESI
6321
APPLIED PROBABILITY
METHODS
IN
ENGINEERING
OEM 2009
January
12,2008
QUIZ
8:009:00AM
Open book
This quiz consists
of 3 problems
Name:
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View Full Document Problem 1: (30 points)
Suppose
that
a
fraction
5%
of
the
microchips
produced
by
a
leading
microchip
manufacturer
is defective.
Historically,
given that a microchip
is defective,
the inspector
(wrongly)
accepts
the chip 10% of the time, thinking
it has no defect. If a microchip
is
not defective,
he always correctly accepts it.
(a) What is the probability that the inspector
accepts a particular microchip?
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(b) Given
that the inspector
accepts
a microchip,
what is the probability)hat
it has no
defect? (If you were unable to answer (l{), please denote the answer to~
by
p).
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Problem 2: (40 points)
The paint department
in an automobile
factory applies two
independent
processes
when
painting
cars: (i) painting and (ii) polishing.
The painting process is defective
20% of the
time, while the polishing process is defective
10% of the time. Each car first goes through
the painting
and then through
the polishing
process.
Each car is inspected
after it has
completed
the two processes.
If
either the painting or the polishing
is defective,
the car is
returned
to a special station for rework,
where the two processes
are applied once,again.
Rework
at the special station is 100% reliable (although it is also very expensive).
(a) What is the probability that a car is returned to the special station for rework?
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(b) Let the random
variable
X
denote
the number of cars in a group
of 1,000 cars that
have painting
defects. Determine
the (exact) distribution,
the expected
value, and the
standard
deviation
of
X
(Do not
only
specify the
type
of distribution
but also all
distribution
parameters!)
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View Full Document (c) Let the random variable
Y
denote the number
of cars in a group of 1,000 cars that
have polishing defects.
The total number of observed
defects
is then equal to
V
=
X +
Y
What is the probability
that the total number of observed
defects is no more than
325?
(Hint:
Can you
use
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This note was uploaded on 05/12/2010 for the course ESI 6321 taught by Professor Josephgeunes during the Spring '07 term at University of Florida.
 Spring '07
 JosephGeunes

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