1. 6.2 – USE NORMAL DISTRIBUTIONS Unit 6 – Data Analysis and Probability

2. Georgia Performance Standards MM3D2a – Determine intervals about the mean that include a given percent of data. MM3D2b – Determine the probability that a given value falls within a specified interval MM3D2c – Estimate how many items in a population fall within a specified interval.

3. Vocabulary

4. Normal Distribution

5. What is Standard Deviation? The standard deviation is a statistic that tells you how tightly all the various examples are clustered around the mean in a set of data. When the examples are pretty tightly bunched together and the bell- shaped curve is steep, the standard deviation is small. When the examples are spread apart and the bell curve is relatively flat, that tells you you have a relatively large standard deviation.

6. Vocabulary

7. Z-scores The z-value for a particular x-value is called the z- score for the x-value and is the number of standard deviations the x-value lies above or below the mean x. To find the probability that z is less than or equal to some given value, use the standard normal table (next slide)

8. Standard Normal Table

9. Example 1: Find a normal probability

10. Finding Normal Probabilities A normal distribution has mean x and standard deviation. Find the indicated probability for a randomly selected x-value from the distribution.

11. Example 2: Interpret normally distributed data The heights of 3000 women at a particular college are normally distributed with a mean of 65 inches and a standard deviation of 2.5 inches. About how many of these women have heights between 62.5 inches and 67.5 inches?

12. Use a z-score and the standard normal table In Example 2 (women going to college), find the probability that a randomly selected college woman has a height of at most 68 inches. Z.0.1.2 -3.0013.0010.0007 -2.0228.0179.0139.1587.1357.1151 -0.5000.4602.4207 0.5000.5398.5793 1.8413.8643.8849

13. Guided Practice for Examples 2 and 3 Guided Practice (Page 221)  4-6