IOE 265 W2007
HW #7
Due: Mon April 2 at 9:00 AM (beginning of lecture)
Please include your name, UM ID and lab section time
in your written homework
assignment. 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. (1 point) p. 265, problem #2.
a.
(0.5 point) Assuming that students buy calculators with the same probability
and independently of each other, then the number
X
of 20 students that
purchase a Texas Instruments calculator is a binomial random variable with
n
= 20 and
p
unknown. However, the sample proportion
ˆ
p
=
X
/
n
is an
unbiased estimator for
p
. In the given sample,
ˆ
p
=
10/20
=
0.5
.
b.
(0.5 point) Following a similar argument to that in part a., the number
Y
of 20
students that own a TI graphing calculator is a binomial random variable with
n
= 20 and
p
’ unknown. However, the sample proportion
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 Winter '07
 Jin
 Normal Distribution, Probability theory, Bias of an estimator

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