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2.4 to 2.5
2.5 to 2.6
2.6 to 2.7
2.7 to 2.8
2.8 to 2.9
2.9 to 3
3 to 3.1
3.1 to 3.2
3.2 to 3.3
3.3 to 3.4
3.4 to 3.5
3.5 to 3.6
3.6 to 3.7
3.7 to 3.8
3.8 to 3.9
3.9 to 4
4 to 4.1
4.1 to 4.2
4.2 to 4.3
4.3 to 4.4
4.4 to 4.5
4.5 to 4.6
4.6 to 4.7
4.7 to 4.8
4.8 to 4.9
4.9>
140
Sampling Distribution of x-bar
120
100
80
60
40
20
0
Again, we notice the bell-curved shape and the decreased range of means (about 2.6 to 4.4)!
Let‟s summarize:
Distribution Type
Original Die Values
UNIFORM
Sampling Distribution
Of 10-Roll Means
NORMAL
Sampling Distribution
Of 20-Roll Means
NORMAL
Sampling Distribution
Of 30-Roll Means
NORMAL
Distribution Mean Distribution Standard Deviation
3.5 1.7
3.5 0.52
3.5 0.38
3.5 0.32
We can very easily see that the expected value of the sampling distribution is the same as , the
expected value of the population distribution. That is:
, ̅-
But, what is the relationship of the standard deviations of the means in relation to the standard
deviation of the population of die roll value!
This is not so clear. Statisticians, after much research, found that the standard deviation of each
of the sampling distribution is related to the sample size in the following way:
Statistics for Decision-Making in Business © Milos Podmanik Page 187