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Z SCORES MM3D3. Recall: Empirical Rule 68% of the data is within one standard deviation of the mean 95% of the data is within two standard deviations.

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Presentation on theme: "Z SCORES MM3D3. Recall: Empirical Rule 68% of the data is within one standard deviation of the mean 95% of the data is within two standard deviations."— Presentation transcript:

1 Z SCORES MM3D3

2 Recall: Empirical Rule 68% of the data is within one standard deviation of the mean 95% of the data is within two standard deviations of the mean 99.7% of the data is within three standard deviations of the mean 2 68% 95% 99.7%

3 Example IQ Scores are Normally Distributed with N(110, 25) Complete the axis for the curve 68% 95% 99.7%

4 Example What percent of the population scores lower than 85? 68% 95% 99.7% %

5 Example What percent of the population scores lower than 100? 68% 95% 99.7%

6 Z Scores

7 Practice: Convert the following IQ Score N(110, 25) to z scores:

8 Z Scores The z score tells you how many standard deviations the x value is from the mean The axis for the Standard Normal Curve:

9 Z Score Table: The table will tell you the proportion of the population that falls BELOW a given z-score. The left column gives the ones and tenths place The top row gives the hundredths place What percent of the population is below.56?.7123 or 71.23%

10 Z Score Table: The table will tell you the proportion of the population that falls BELOW a given z-score. The left column gives the ones and tenths place The top row gives the hundredths place What percent of the population is below.4?.6554 or 65.54%

11 Practice: Use your z score table to find the percent of the population that fall below the following z scores: 1. z < z < z < z < z < % % % % 5..03%

12 Using the z score table You can also find the proportion that is above a z score Subtract the table value from 1 or 100% Find the percent of the population that is above a z score of 2.59 z > or.48% Find the percent of the population that is above a z score of z > or 97.19%

13 Using the z score table You can also find the proportion that is between two z scores Subtract the table values from each other Find the percent of the population that is between.27 and < z < or 30.35% Find the percent of the population that is between and < z < or 94.84%

14 PRACTICE WORKSHEET

15 Application 1

16 Application 2

17 Application 3

18 PRACTICE WORKSHEET


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