1 / 22

The Normal Distribution (Gaussian Distribution)

The Normal Distribution (Gaussian Distribution). Honors Analysis. Learning Target: I can analyze data using the normal distribution. German mathematician Influenced statistics, algebra, number theory, geometry, physics. Child prodigy! Constructed heptadecagon Triangular numbers

tayten
Download Presentation

The Normal Distribution (Gaussian Distribution)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. The Normal Distribution(Gaussian Distribution) Honors Analysis Learning Target: I can analyze data using the normal distribution.

  2. German mathematician • Influenced statistics, algebra, number theory, geometry, physics. • Child prodigy! • Constructed heptadecagon • Triangular numbers • Proved Fundamental Theorem of Algebra • Influenced development of statistics, including Normal Distribution (Gaussian Distribution) Carl Friedrich Gauss (1777-1855)

  3. Imagine you took a test in two different classes. • In the first class, you made a 93%. The class mean was a 96%, and the standard deviation was 3%. • In the second class, you made a 78%. The class mean was a 74%, and the standard deviation was 2%. Which test performance was better?

  4. Normal Distribution(Gaussian Distribution)

  5. (Approximately) 68% within 1 std dev. of mean • 95% within 2 std. deviations of mean • 99.7% fall within 3 standard deviations of mean 68-95-99.7 Rule

  6. Calculate the mean (central value on curve) • Each region increases or decreases by one standard deviation from the mean • Ex: Test score mean: 74% Std. dev: 2% Labeling a Simple Normal Curve

  7. So what happens if you want to calculate a percentage for a value that ISN’T on your normal curve? • Ex: PSAT math test with mean of 48 and a std. deviation of 3. What percent of scores are below 50?

  8. Normal distribution with a mean of 0 and a standard deviation of 1. • Total area under curve = 1 • Area to left of a given value on the curve gives the percentile rank – percent of scores LOWER than a given score. Standard Normal Distribution

  9. You can convert values to standard normal distribution form by calculating a z-score: • Z-Score percentages can be looked up in a table or on a calculator. Z-Scores

  10. Example

  11. Solution

  12. Example Part II

More Related