#1. a) What proportion of a normal distribution is within one standard deviation of the mean? b) What proportion is more than 1.8 standard deviation from the mean? c) What proportion is between 1 and 1.5 standard deviation above the mean? #4. #2. If scores are normally distribution with the mean of 30 and the standard deviation of 5, what percent of the scores is a) greater than 30? b) equal to 302 a) greater than 377 d) between 28 and 34? #3. A test is normally distributed with the mean of 40 and the standard deviation of 7. a) What score would be needed to be in the 85-th percentile? b) What score would be needed to be in the 22-th percentile? You plan to open a men's closing store. To minimize startup costs, you will not stock suits for the tallest 10% and the shortest 10% of men. Men's heights are normally distributed with the mean 69.0 inches and the standard deviation of 2.8 inches. Find the minimum and maximum heights of the men for whom suits will be stocked. #5. SAT test scores are normally distributed with a mean of 509 and a standard deviation of 112. a) if one student is randomly selected, find the probability that his score is at least 590. b) If 16 students are randomly selected, find the probability that their mean score is at least 590. #6. College students annual earnings are normally distributed with standard deviation = $ 640. If the mean earning for group of 64 students is $ 4000, construct a 95% confidence interval estimate of the mean annual earnings for all college students.