Sample Final Exam II 1 ) It is known that the distribution of grades of a reading test for ten year olds is normally distributed with mean = 90 and standard deviation = 15. Find the percentage of ten year olds who get grades: a) Between 60 and 120. b) Under 114 c) Over 60 d) Over 150 e) Find the 30th percentile. 2) The mean weight of members of a Weight Watchers chapter is 250 Ibs. The standard deviation is 24 lbs. If a sample of 36 members is taken, find the probability that: a) The mean weight is more than 260 lbs. b) The mean weight of the sample is within 4 lbs. of 250. " . ... 3) A sample of 16 overweight people uses a new reducing pill for 6 weeks and has a mean weight loss of 20 lbs. The standard deviation is 8 Ibs a) Find a 95% confidence interval for the mean weight loss. b) If the same information was found using a sample of 50, how would that affect the length of the confidence interval? 4) A sample of 64 students in a school district have a mean score of 515 on the Math SAT Exam. The standard deviation is 96. a) Find a 99 % confidence interval for the mean SAT score b) If we we used a 95 % confidence level, how would that affect the length of the confidence interval? 5) A study is taken, to see if teacher's salaries are lower in New York City than in the rest of the state. In New York State the mean salary for teachers is $48,500 with standard deviation of $9,000. A sample of 36 New York City teachers has a mean salary of $47,200. At the 1 % significance level, is the data sufficient to justify the assertion that New York City teachers salaries are lower. Justify your