# Normal Distribution and the Standard Deviation

- Author:
- Kathryn Shafer

The GeoGebra applet contains a random normal distribution with 100 data points.

- Randomize the data at least 10 times. What do you notice about the shape of the distribution? Share with a classmate.
- Use the movable lines to estimate the location of -1 stdev, the mean, and +1 stdev in the distribution. How did you decide where to put the lines? Click in the Show Statistics checkbox and compare your estimates to the actual +/-1 stdev range.
- Hide the statistics and repeat step (a) at least ten more times.
- Did you change your strategy? Explain.
- Position the movable lines at the ends of the +/-1 stdev range.
- Estimate the number of data points captured in the +/-1 stdev range. Click on the Show Count checkbox and compare the actual count to your estimate.
- Hide the count information and repeat step (a) at least ten more times. What do you notice?
- If a normal distribution has 1,000 points, what percentage would you expect to be in the +/-1 stdev range? Explain.

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