1. Section 2.2, Part 1 Standard Normal Calculations AP Statistics Berkley High School/CASA

2. AP Statistics, Section 2.2, Part 12 Comparing data sets How do we compare results when they are measured on two completely different scales? One solution might be to look at percentiles What might you say about a woman that is in the 50 th percentile and a man in the 15 th percentile?

3. AP Statistics, Section 2.2, Part 13 Another way of comparing Another way of comparing: Look at whether the data point is above or below the mean, and by how much. Example: A man is 64 inches tall. The heights of men are normally distributed with a mean of 69 inches and standard deviation of 2.5 inches.

4. AP Statistics, Section 2.2, Part 14 Another way of comparing Example: A man is 64 inches tall. The heights of men are normally distributed with a mean of 69 inches and standard deviation of 2.5 inches. We can see that the man is below the mean, but by how much?

5. AP Statistics, Section 2.2, Part 15 Another way of comparing Example: A man is 64 inches tall. The heights of men are normally distributed with a mean of 69 inches and standard deviation of 2.5 inches.

6. AP Statistics, Section 2.2, Part 16 z-scores The z-score is a way of looking at every data set, because each data set has a mean and standard deviation We call the z-score the “standardized” score.

7. AP Statistics, Section 2.2, Part 17 z-scores Positive z-scores mean the data point is above the mean. Negative z-scores mean the data point is below the mean. The larger the absolute value of the z-score, the more unusual it is.

8. AP Statistics, Section 2.2, Part 18 Using the z-table We can use the z- table to find out the percentile of the observation. A z-score of -2.0 is at the 2.28 percentile.

9. AP Statistics, Section 2.2, Part 19 Cautions The z-table only gives the amount of data found below the z-score. If you want to find the portion found above the z-score, subtract the probability found on the table from 1.

10. AP Statistics, Section 2.2, Part 110 Standardized Normal Distribution We should only use the z-table when the distributions are normal, and data has been standardized N(μ,σ) is a normal distribution N(0,1) is the standard normal distribution “Standardizing” is the process of doing a linear translation from N(μ,σ) into N(0,1)

11. AP Statistics, Section 2.2, Part 111 Example Men’s heights are N(69,2.5). What percent of men are taller than 68 inches?

12. AP Statistics, Section 2.2, Part 112 Working with intervals What proportion of men are between 68 and 70 inches tall?

13. AP Statistics, Section 2.2, Part 113 Working backwards How tall must a man be in order to be in the 90 th percentile?

14. AP Statistics, Section 2.2, Part 114 Working backwards How tall must a woman be in order to be in the top 15% of all women?

15. AP Statistics, Section 2.2, Part 115 Working backwards What range of values make up the middle 50% of men’s heights?

16. AP Statistics, Section 2.2, Part 116 Assignment Exercises 2.19 – 2.25, The Practice of Statistics.

17. AP Statistics, Section 2.2, Part 117

18. AP Statistics, Section 2.2, Part 118

19. AP Statistics, Section 2.2, Part 119

20. AP Statistics, Section 2.2, Part 120