1. 7.4 (Purple) Use Normal Distributions Midterm: TOMORROW *Answers to the review book work is on my teacher page* Statistics Quiz: Friday

2. Vocabulary Normal Distribution –Is modeled by a bell-shaped curve called a normal curve that is symmetric about the mean. The total area under the related curve is 1. The percentage of the area covered by each standard deviation from the mean is shown in the graph. (on the next slide).

3. Graph of a Normal Curve: You need to know this!

4. Vocabulary Standard Normal Distribution Is the normal distribution with mean 0 and standard deviation 1. On p. 264 in your textbook

5. Formula The formula below can be used to transform x-values from a normal distribution with mean x and standard deviation σ into z-values having a standard normal distribution. On p. 264 in your textbook

6. Z-Value The z-value for a particular x-value is called the z-score for the x-value and is the number of standard deviation the x-value lies above or below the mean x. ***To use the z-score you will need to look at the table that is on p. 296 in your textbook***

8. Example 1: A normal distribution has mean x and standard deviation σ. Find the indicated probability for a randomly selected x-value from the distribution. P(x > x + σ) P(x < x < x + σ)

9. You Try: A normal distribution has mean x and standard deviation σ. Find the indicated probability for a randomly selected x-value from the distribution. 1.1. P ( ≤ )xx 2.2. P( > )xx 3.3. P( – σ < x < )xx 4.4. P (x ≤ – 3σ) x

10. Example 2: The heights (in feet) of fully grown white oak trees are normally distributed with a mean of 90 feet and a standard deviation of 3.5 feet. –About what percent of white oak trees have heights between 86.5 feet and 93.5 feet?

11. Example Cont’d –Find the probability that a randomly selected white oak tree has a height of at most 94 feet. –You need to find the z-score (use the formula) Look at the Standard Normal Table

12. You Try: For the following questions, refer to Example 2. 1.About what percent of white oak trees have heights less than 97 feet? 2.About what percent of white oak trees have heights between 83 feet and 90 feet? 3.Find the probability that a randomly selected white oak tree has a height of at most 85 feet.

13. Homework Review for Midterm *Answers to the review book work is on my teacher page* MIDTERM TOMORROW!