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EMPIRICAL RULE 68-95-99.7 RULE Ch. 6 Day 3 AP Statistics EQ: What is the empirical rule and why do we need it? DENSITY CURVE Properties Total area under the curve is 1 It lies on or above the horizontal axis It describes the overall pattern of distribution Areas under the curve represent proportions of observations EMPIRICAL RULE 68% of your data falls within 1 standard deviation of the mean. 95% of your data falls within 2 standard deviations of the mean. 99.7% of your data falls within 3 standard deviations of the mean. STEPS TO FOLLOW 1. 2. 3. 4. What question are you answering? Check conditions. Mechanics(picture clearly labeled) Conclusion 1. 2. 3. Assuming the heights of college women are normally distributed with mean = 65” and std dev = 2.5”: What percentage of women are taller than 70 inches? What proportion of women are shorter than 67.5 inches? What percentage of women are between 60 and 72.5 inches? The distribution of SAT Math or Verbal scores is normally distributed with mean 500 and standard deviation 100. Suppose you earn a 600 on one part of your SAT. Where do you stand among all students who took that test? What proportion of SAT scores fall between 450 and 600? Suppose a college says it admits only people with SAT Verbal test scores among the top 15%. How high a score does it take to be eligible? NORMAL PROBABILITY PLOT If the distribution of data is roughly Normal, the plot is roughly a diagonal straight line Deviations from a straight line indicate that the distribution is not Normal WHAT CAN GO WRONG? 1. 2. 3. 4. 5. Don’t use a Normal model when the distribution is not unimodal and symmetric. Don’t use the mean and standard deviation when outliers are present. Don’t round too soon! Don’t round your results in the middle of calculation. Don’t worry about minor differences in results. HOMEWORK P. 129 # 26, 30, 46 Uniform Distribution Worksheet