IOE 265 W2007
HW #5 Solutions
Due: Wed March 7 at 9:00 AM (beginning of lecture)
Please include your name, UM ID and lab section time
in your written homework
assignment. The assignment is worth 20 points (double the usual amount). You may
work with other students to discuss problem approaches and check answers, but you
may not copy another’s work or refer to solutions from the Instructor’s manual or
solutions from previous semesters. Please be sure to staple your assignment if it
includes multiple pages.
All problems are from the Devore text, 6
th
edition.
1. (2.5 points) p. 150, problem #6.
a.
(0.5 point)
b.
(0.5 point)
k
1
"
(
x
"
3)
2
[ ]
dx
2
4
#
=
1
$
k
(1
"
x
2
+
6
x
"
9)
dx
2
4
#
%
’
(
)
*
=
1
$
k
"
x
3
3
+
3
x
2
"
8
x
[ ]
2
4
=
1
$
k
8
3
"
64
3
+
48
"
12
"
32
+
16
( )
=
1
$
k
=
3
4
c.
(0.5 point) Since the prescribed weight is equal to the mean, and this pdf is
symmetric about the mean, the probability that the actual weight exceeds the
prescribed weight is 0.5.
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View Full Documentd.
(0.5 point) First, it is helpful to obtain the cdf of
X
, which is (for 2<x<4)
F
(
x
)
=
k
"
y
3
3
+
3
y
2
"
8
y
[ ]
2
x
=
"
y
3
4
+
9
4
y
2
"
6
y
[ ]
2
x
=
"
x
3
4
+
9
4
x
2
"
6
x
+
5
.
Then the probability that the actual weight is within .25 g of the prescribed
weight is
F
(3.25)
F
(2.75) = 0.367.
e.
(0.5 point) Again using the cdf computed in d), the probability that the actual
weight differs from the prescribed weight by more than .5 g is 1(
F
(3.5)
F
(2.5)) = 1.688 = .312.
2. (3 points) p. 159, problem #18.
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 Winter '07
 Jin
 Normal Distribution, DeVore

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