Rachel Baker
BIOS 600 001
Homework 3
2/11/10
Problem
1
(ii) Means of samples of size n=2:
The histogram of means is spread out (large standard deviation) and skewed to the right,
or the mean is larger than the median.
Mean = 16.99
sd = 6.72
(iii) Means of samples of size n=5:
The histogram of means has a moderate spread (range) and slightly skewed to the right,
or the mean is slightly larger than the median.
Mean = 15.97
sd = 4.33
(iv) Means of samples of size n=25:
The histogram of means approximates the normal distribution, although it is slightly
skewed to the left. The histogram shape is very centralized around the sample mean with
a relatively small standard deviation and spread (range).
Mean = 15.71
sd = 2.01
(v) Theoretical values should only be approximated by Central Limit Theorem for n >
25.
Theoretical mean:
µ
, the mean of the original distribution (16)
Theoretical standard deviation: √(σ²/
n)
, where σ² is the variance of the original
distribution (90.666), and
n
the sample size.
Sample Size
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 Spring '08
 Staff
 Central Limit Theorem, Normal Distribution, Standard Deviation, Rachel Baker

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