Statistics for Decision- Making in Business - Maricopa Community ...

1.7 to 1.8
1.8 to 1.9
1.9 to 2
2 to 2.1
2.1 to 2.2
2.2 to 2.3
2.3 to 2.4
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
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4.6 to 4.7
4.7 to 4.8
4.8 to 4.9
4.9 to 5
5 to 5.1
5.1 to 5.2
5.2>
2.4 to 2.65
2.65 to 2.9
2.9 to 3.15
3.15 to 3.4
3.4 to 3.65
3.65 to 3.9
3.9 to 4.15
4.15 to 4.4
4.4 to 4.65
4.65 to 4.9
4.9 to 5.15
5.15>
6
Sampling Distribution of x-bar
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4
3
2
1
0
This is quite interesting… we have obtained a distribution (of means) that appears somewhat
bell-shaped.
Suppose now that we had a total of 1000 people roll a die 10 times each, and to then compute the
sample mean. Here is what a simulation of this process would look like:
100
90
80
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60
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40
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10
0
Sampling Distribution of x-bar
Wow! Our distribution of means for 1000 individuals for experiments of 10 rolls each produces
something remarkably like a normal distribution. Additionally, it appears that the mean of this
distribution is around 3.5!
Let‟s try this again, but now, let‟s say that 1000 individuals each roll a die 20 times, and each
individual computes a sample mean. This simulated event would produce the following
distribution of die-roll average:
Statistics for Decision-Making in Business © Milos Podmanik Page 185