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Integrated Math 1 - Unit 8 Name: __________________________ 8.6B – Introduction to the Normal Model Date: _____________ Period: ______ Objective: Applying the Empirical Rule to Normal data. Let’s look back at the histogram of IQ scores: IQ scores between _________ and __________ fall within 1 standard deviation of the mean. IQ scores between _________ and __________ fall within 2 standard deviations of the mean. IQ scores between _________ and __________ fall within 3 standard deviations of the mean. So, why don’t we go out further than 3 standard deviations? The Empirical Rule (68-95-99.7 Rule): 68% of the data fall within 1 standard deviation of the mean 95% of the data falls within 2 standard deviations of the mean 99.7% of the data falls within 3 standard deviations of the mean Only ___________% of the data will fall outside of 3 standard deviations. This is such an insignificant amount, so it is not necessary to include values that fall outside of 3 standard deviations. Let’s practice using the Empirical Rule given a Normal distribution! Examples: 1. Suppose that the mean height for women is 65 inches with a standard deviation of 3 inches. a) Draw and label a Normal curve for the heights of women. b) What percent of women’s heights fall between 59 in. and 71 in.? c) The mean height for men is 70 inches. If 68% of men’s heights fall between 65 in. and 75 in., what is the standard deviation for the men? 2. In Witchita, Kanas, the mean high temperature in July is shown by the Normal distribution: a) What is the mean high temperature in July? b) What is the standard deviation? 79.9 83.8 87.7 c) What percentage of data falls between 87.7 and 95.5? CHALLENGE: What percentage of data fall above 83.8? 91.6 95.5 99.4 103.3