Normal Distribution vs Standard Normal Distribution:
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When you hear the term normal distribution, you probably think about the perfect bell shape.
However, not all Normal distributions are perfectly shaped.
They are usually stretched or squeezed and moved horizontally right or left.
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However, not all Normal distributions are perfectly shaped.
They are usually stretched or squeezed and moved horizontally right or left.
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What are the effecting factors?
- Mean determines the center of the curve.
Increasing the mean will move the curve to the right.
- Standard deviation stretches or squeezes the curve.
A small standard deviation results in a narrow curve.
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- Mean determines the center of the curve.
Increasing the mean will move the curve to the right.
- Standard deviation stretches or squeezes the curve.
A small standard deviation results in a narrow curve.
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Here are some examples.
A (M = 0, SD = 1) Standard normal distribution
B (M = 0, SD = 0.5) Squeezed, because SD < 1
C (M = 0, SD = 2) Stretched, because SD > 1
D (M = 1, SD = 1) Shifted right, because M > 0
E (M = –1, SD = 1) Shifted left, because M < 0
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A (M = 0, SD = 1) Standard normal distribution
B (M = 0, SD = 0.5) Squeezed, because SD < 1
C (M = 0, SD = 2) Stretched, because SD > 1
D (M = 1, SD = 1) Shifted right, because M > 0
E (M = –1, SD = 1) Shifted left, because M < 0
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Now it is time to answer our question.
What is the difference then?
- Normal distribution can take on any value as its mean and standard deviation.
- In the standard normal distribution, the mean and standard deviation are always fixed.
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What is the difference then?
- Normal distribution can take on any value as its mean and standard deviation.
- In the standard normal distribution, the mean and standard deviation are always fixed.
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The standard normal distribution is a special normal distribution where:
- The mean is 0
- The standard deviation is 1
It is also called the z-distribution.
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- The mean is 0
- The standard deviation is 1
It is also called the z-distribution.
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