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View Full Document IOE 265 F2006
Exam I
6 of 10
14.
A plan for an executive travelers’ club has been developed by an airline on the
premise that 10% of its current customers would qualify for membership
a.
Assuming the validity of this premise, among 25 randomly selected current
customers, what is the probability that between 2 and 6 (inclusive) qualify for
membership?
Let
X
be the number among the 25 customers who are qualified for membership.
Then
X
has a binomial distribution with
n
=25 and
p
=.10. Thus,
P
(2
≤
X
≤
6) = B(6; 25,
.1)  B(1; 25, .1) = .991  .271 = .720.
Note that the binomial cdf tables were used in the solution, but one could have
computed the probability directly from the pmf as well.
b.
Again assuming the validity of the premise, what are the expected number of
customers who qualify and the standard deviation of the number who qualify
in a random sample of 100 current customers?
Now let
Y
be the number among the 100 customers who qualify. Then
Y
has a
binomial distribution with
n
=100 and
p
=.10. By definition,
E
(
Y
) =
np
= 10 and
"
Y
=
V
(
Y
)
=
np
(1
#
p
)
=
100(.9)(.1)
=
3
c.
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This note was uploaded on 01/18/2009 for the course IOE 265 taught by Professor Jin during the Winter '07 term at University of Michigan.
 Winter '07
 Jin

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