1. Honors Advanced Algebra Presentation 1-6

2. Vocabulary

3. Z-Scores

4. Example 1 Find the z-score of a data point of 21 when the mean is 24 and the standard deviation is 2

5. Example 2 Find the z-score of a data point of 58 when the mean is 50 and the standard deviation is 3.5

6. Analyzing Z-Scores Z-scores are interpreted from a z-score table. The table tells the area of the curve to the left of a z- score.

7. Example 3 If a data point has a z-score of.5, what is the probability of getting lower than that score?

8. Example 4 If a data point has a z-score of -1, what is the probability of getting higher than that score?

9. Example 5 What is the probability of getting a score between the z-score of -1 and the z-score of.5?

10. Example 6 Scores on a test are normally distributed with a mean of 75 and a standard deviation of 8. 1. Estimate the probability that a randomly selected student scored less than an 87. 2. Estimate the probability that a randomly selected student scored more than a 79.

11. Example 6 (cont’d) Scores on a test are normally distributed with a mean of 75 and a standard deviation of 8. 3. Estimate the probability that a randomly selected student scored between 71 and 75.

12. Example 7 Heights of females are normally distributed with a mean of 5’4” with a standard deviation of 2.7 inches. 1. What is the probability that a randomly selected female will be shorter than 5’? 2. What is the probability that a randomly selected female will be taller than 6’?

13. Example 7 (cont’d) Heights of females are normally distributed with a mean of 5’4” with a standard deviation of 2.7 inches. 3. What is the probability that a randomly selected female will be between 5’2” and 5’8”? 4. What is the probability that a randomly selected female will be either shorter than 5’2” or taller than 5’8”?

14. Example 7 (cont’d) Heights of females are normally distributed with a mean of 5’4” inches with a standard deviation of 2.7 inches. 5. If a female’s height gave her a z-score of 2.3, how tall was she? 6. If a female wants to be taller than 99.3% of other females, how tall does she have to be?