Introduction to Normal Distribution

• Go to www.socr.ucla.edu
• Click the "Distributions" tab
• In the drop-down menu on the left, select Normal Distribution

You should see something like this:

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• This is the standard normal distribution. In this distribution, the mean, median, and mode all appear at the center. Half of the data falls into the left side of the center and half falls into the right side.
• In the picture above, the distribution has a mean of 0, and a standard deviation of 50.
• If you scroll down, you will see a box labeled "Left Cut Off" and another labeled "Right Cut Off." You can use these to find what percent of the values fall between certain values.
• Try typing -50 in the left cutoff box and 50 in the right cutoff box. You must hit "Enter" after you type in each value. This represents the area between -1 standard deviation and +1 standard deviation. You should see something like this:

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• Notice in the green box below the graph there are several values listed. It says Between: .682689. This means that about 68.27% of the data lies between -1 and +1 standard deviations.
• It also lists how much of the data lies to the left of -1 standard deviation and to the right of +1 standard deviation.

• Now set the left cutoff at -100 and the right at 100. Don't forget to hit Enter after you change your data! Here's what you will see:

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