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Recall the empirical rule (66-95-99.7 Rule) as followed: 99.7% of the data are within 3 standard deviations of the mean 95% within 2 standard deviations 68% within 1 standard deviation 1 - 30 1 - 20 1 + 30 H - G 1 + 20 Given an approximately normal distribution with mean of 159 and a standard deviation of 17. a: Complete the graph above by writing the correspond values of u - 30, H - 20, H - O, H, u to, u + 20 and u + 30. You may write the values under it. b: What percent of the values are within the interval (142, 176)? c: What percent of the values are within the interval (125, 210)? d: What percent of the values are below 159? e: What percent of the values are above 176? Section 6.1: The Standard Normal Distribution 4: Find the area of the shade region.a: What proportion of test takers score a 130 or higher? b: What score would begin the interval for the top 16% of all scores? c: The top 10% of all scores represent the label of "genius". What is the range of scores for anyone who qualifies as a genius? 9: Assume the cholesterol levels of adult American women can be described by a normal distribution with a mean of 188 mg/dL and a standard deviation of 24 mg/dL. a: What percent of adult women do you expect to have cholesterol levels over 200 mg/dL? b: What percent of adult women do you expect to have cholesterol levels between 150 and 170 mg/dL? c: Above what value are the highest 15% of women's cholesterol levels? Section 6.3: Sampling Distributions and Estimators 10: Let the population consists of three data points: {2, 3, 7}. a: Calculate the population mean, population variance and population standard deviation. b: If we would like to take two numbers with replacement, (This means after you pick your first number, you have to replace the number you picked and then pick your second number.) list all 9 possible ways of getting two numbers. c: For each of the sample from part b, calculate the sample mean. Denote them as T 1a: What proportion of test takers score a 130 or higher? b: What score would begin the interval for the top 16% of all scores? c: The top 10% of all scores represent the label of "genius". What is the range of scores for anyone who qualifies as a genius? 9: Assume the cholesterol levels of adult American women can be described by a normal distribution with a mean of 188 mg/dL and a standard deviation of 24 mg/dL. a: What percent of adult women do you expect to have cholesterol levels over 200 mg/dL? b: What percent of adult women do you expect to have cholesterol levels between 150 and 170 mg/dL? c: Above what value are the highest 15% of women's cholesterol levels? Section 6.3: Sampling Distributions and Estimators 10: Let the population consists of three data points: {2, 3, 7}. a: Calculate the population mean, population variance and population standard deviation. b: If we would like to take two numbers with replacement, (This means after you pick your first number, you have to replace the number you picked and then pick your second number.) list all 9 possible ways of getting two numbers. c: For each of the sample from part b, calculate the sample mean. Denote them as $1 = 13 =CA = 15 = Do = 27 = C8 = d: Find the mean of the sample means from part c. e: For each of the sample from part b, calculate the sample variance (not standard deviation). Denote them as ST = $2 = SA SY = f: Find the mean of the sample variances from part e. g: For each of the sample from part b, calculate the sample standard deviation. Denote them as $1 = $2 = S3 = S4 = $5 = S8 = Sg = h: Find the mean of the sample standard deviations from part g