Statistics 5021 – Homework 3
There are 20 total points (1 point for each part of each question and 3 points for handing
in the assignment). One question will be graded for correctness. This homework is due
Thursday, February 17 in your lab section.
1. Deﬁne the following terms.
(a) Random sample
(b) Realization of a random sample
2. Suppose that we model the time, in minutes, it takes to drive from Apple Valley to
the University of Minnesota during rush hour with the
N
(
μ
= 44
,σ
= 8) distribution.
In particular, 86 individuals plan to make this drive. Let
X
1
,...,X
86
denote the
yettobe measured drive times. Assume that
X
1
,...,X
86
are a random sample from
N
(
μ
= 44
,σ
= 8).
(a) What is the the probability distribution of the sample mean drive time of these 86
individuals who plan to make this drive? (specify the values of its parameters).
(b) What is the name of the probability distribution of the random variable:
¯
X

44
8
/
√
86
(c) What is the probability that we will observe a sample mean of at least 45 minutes
based on this sample of size 86?
1
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View Full Document(d) One can use
R
to simulate the probability computed in problem 2c. This is done
by generating
reps
= 10
5
realizations of a random sample from
N
(
μ
= 44
,σ
= 8),
and computing the proportion of these realizations for which the observed sample
mean was at least 45 minutes. Run the following
R
code (you may copy and paste
it) to compute the simulated value of
P
(
¯
X
≥
45). Compare this value to that
computed in problem 2c.
reps=10^5
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 Spring '08
 Staff
 Statistics, Normal Distribution, Standard Deviation, Variance, Probability theory, probability density function

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