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Thinking Mathematically Statistics: 12.4 The Normal Distribution Remember mean and standard deviation? Exercise Set 12.4 #5 A set of test scores are normally distributed with a mean of 100 and a standard deviation of 20. Find the score that is 21/2 standard deviations above the mean. The 68-95-99.7 Rule for the Normal Distribution 99.7% 95% 68% -3 -2 -1 1 2 3 The 68-95-99.7 Rule for the Normal Distribution 1. Approximately 68% of the measurements will fall within 1 standard deviation of the mean. 2. Approximately 95% of the measurements will fall within 2 standard deviations of the mean. 3. Approximately 99.7% (essentially all) the measurements will fall within 3 standard deviations of the mean. Examples: The 68%, 95%, 99.7% Rule Exercise Set 12.4 #15, #25 The mean price paid for a particular model of car is $17,000 and the standard deviation is $500 (see graph in text). Find the percentage of buyers who paid between $16,000 and $17,000. IQs are normally distributed with a mean of 100 and a standard deviation of 16. Find the percentage of scores between 68 and 100. Computing z-Scores A z-score describes how many standard deviations a data item in a normal distribution lies above or below the mean. The z-score can be obtained using z-score = data item – mean standard deviation Data items above the mean have positive z - scores. Data items below the mean have negative z-scores. The z-score for the mean is 0. Exercise Set 12.4 #35 A set of data items is normally distributed with a mean of 60 and a standard deviation of 8. What is the z score for 84? Thinking Mathematically Statistics: 12.4 The Normal Distribution