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Econ 15B
Assignment 1
Ghosh
UC Irvine
(Total 50 points)
Due 08/10/10
Chapter 9:
9.5 (8
th
edition):
(10 points)
A normally distributed population has a mean of 40 and a standard deviation of 12. What does the central
limit theorem say about the sampling distribution of the mean if samples of size 100 are drawn from this
population?
ANS: The sampling distribution of the mean is normal with a mean of 40 and a standard
deviation of 12/
100 = 1.2.
9.10 (8
th
edition):
(10 points)
Given a normal population whose mean is 50 and whose standard deviation is 5,
a. find the probability that a random sample of 4 has a mean between 49 and 52.
b. find the probability that a random sample of 16 has a mean between 49 and 52.
c. find the probability that a random sample of 25 has a mean between 49 and 52.
ANS: a.
=
<
<
)
52
X
49
(
P
−
<
σ
µ
−
<
−
4
/
5
50
52
n
/
X
4
/
5
50
49
P
= P(–.40 < Z < .80)
= P(Z < .80)
− P(Z < −.40) = .7881 −.3446 = .4435
b.
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