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Review Exam 3 Math 115 Fall 05 1) 4400 college graduates are questioned about the lengths of time required to earn their bachelor’s degrees. The mean is 5.15 years and the population standard deviation, σ, is 1.68 years. Based on these sample data, construct the 99% confidence interval for the mean time required by all college students. (5.08 < < 5.22) 2) In the design of a vending machine we want the machine to accept coins of a certain weight only. We weigh 22 quarters and find the mean to be 5.622 g with a sample standard deviation of 0.068 g. Based on this random sample, determine the 90% confidence interval for the mean weight of a quarter. (5.597 < < 5.647) 3) Radio station WLSD is considering a change in its format. In a survey of 1500 randomly selected people, 63% indicated that they listen to their favorite radio station because of the music played. Construct the 98% interval estimate of the true population percentage of all people who listen to their favorite radio station because of the music played. (60.1% < P < 65.9%) 4) Eleven members of an elite, highly intelligent group of left handed people are given an IQ test with the following scores noted: 124, 133, 141, 129, 122, 131, 138, 122, 130, 127, and 129. Determine the 99% confidence interval for the mean IQ of the entire group. (The population is normally distributed) (123.8 < < 135.4) 5) We wish to determine the percentage of individual tax returns that included capital gains deductions. How many such returns must be randomly selected and checked? We need to be 90% confident that the sample percent is in error by no more than 4 percentage points. (423) 6) We wish to determine the mean value of cars owned by retired people. If we wish to be 96% confident that the mean value of the sample group is off by no more than $250, how many retired people must be sampled? A prior study suggests that the sample standard deviation is $3050. (626) 7) The We Never Pay insurance company is suspicious about a cluster of Clinton County deaths that resulted from oxygen poisoning. The company wishes to estimate the proportion of home accident deaths caused by oxygen poisoning. How many such deaths must be surveyed to be 95% confident that the sample proportion is within 0.04 of the true population proportion? (601) For the following problems use the fact that IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. 8) What is the probability of selecting someone at random with an IQ score greater than 120? 9) What is the probability of selecting someone at random and their IQ score is less than 110? 10) What is the probability of a sample of 45 people having a mean IQ score between 95 and 105? 11) What is the probability of a sample of 103 people having a mean IQ score greater than 120? 12) What is the probability of a sample of 300 people having a mean IQ score less than 85?