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1. Y=sq rt(x)
2. Y does not appear to have a uniform distribution because not all of the values are
equally likely. There is also not a Normal distributionthe histogram is skewed to the left.
The heights of the histogram bars generally increase as the value of Y increases. This is
because the graph of Y=sqrt(x) generally increases as x increases.
3.
The mean is therefore also around .663 and the standard deviation is
σ/sqrt(n)=.234915/sqrt(200)=.0166. However, this method cannot be used because this is
not a normal model. So the actual standard deviation is probably closer to the sample
standard deviation.
4.This is very close to the actual mean(2/3 is about .667) and the actual standard
deviation (1/sqrt(18)=.2357).
II
N
Exact
mean
Mean
(YBAR
)
Exact SD
SD
(YB
AR)
Exact variance
Variance
(YBAR)
1
2/3
.663
1/sq rt(18)
.2349
1/18
(.2349)
2
=
.055
5
2/3
.668
(1/sqrt(18))/sqrt(5)
.106
.0111
.0112
10
2/3
.676
(1/sqrt(18))/sqrt(10)
.074
1/10
2
x (10 x 1/18)
.0055
40
2/3
.669
(1/sqrt(18))/sqrt(40)
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 Fall '08
 STAFF
 Normal Distribution

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