# Z SCORES MA2D3. 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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Z SCORES MA2D3

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%

Example IQ Scores are Normally Distributed with N(110, 25) Complete the axis for the curve 68% 95% 99.7% 110 135 160 185 85 60 35

Example What percent of the population scores lower than 85? 68% 95% 99.7% 110 135 160 185 85 60 35 16%

Example What percent of the population scores lower than 100? 68% 95% 99.7% 110 135 160 185 85 60 35 100

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: 01 2 3 -2 -3

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%

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%

Practice: Use your z score table to find the percent of the population that fall below the following z scores: 1. 2.01 2. 3.39 3. 0.08 4. -1.53 5. -3.47 1. 97.78% 2. 99.97% 3. 53.19% 4. 6.30% 5..03%

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 1-.9952.0048 or.48% Find the percent of the population that is above a z score of -1.91 1-.0281.9719 or 97.19%

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 1.34.9099-.6064.3035 or 30.35% Find the percent of the population that is between -2.01 and 1.89.9706-.0222.9484 or 94.84%

PRACTICE WORKSHEET

Z Scores

Practice: Convert the following IQ Score N(110, 25) to z scores: 1. 100 2. 125 3. 75 4. 140 5. 45 1. -.4 2..6 3. -1.4 4. 1.2 5. -2.6

Application 1

Application 2

Application 3

PRACTICE WORKSHEET

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