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1.) Standardized IQ test scores are normally distributed with a sample mean of 100 and a sample population of 15. Find the following: a.) Find the probability that a randomly selected person has an IQ higher than 117. b.) Out of 2000 randomly selected people, about how many would you expect to have a score lower than 93? c.) What is the lowest score that would still place a person in the top 5% of the scores? Now assume from past studies of IQ scores that the population standard deviation was calculated to be 14.8. Remember the population mean and sample mean are the same. d.) Construct an 80% confidence interval around the population mean. e.) Construct a 96% confidence interval around the population mean. 2.) In a survey of 2016 US adults, 1310 think the mainstream media is more interested in making money than telling the truth. a.) Find a 99% confidence interval for the population proportion. b.) You want to produce your own results with a 95% confidence and you want your estimate to be within 5% of the population proportion. If no preliminary estimate is available, find the minimum sample size needed. 3.) In a survey of 3539 US adults, 53% believed that the economy was improving. The survey's margin of error isi3%. a.) Translate the statement into a confidence interval. b.) Approximate the level of confidence (at what percent). 4.) Final exam scores for a past statistics course is listed below. Assume that this sample size is from a normally distributed population. 59 71 65 59 90 55 61 73 59 99 83 60 87 64 48 67 40 55 Show your work necessary to solve 68 69 97 43 61 87 a.) Find a confidence interval around the mean. Determine a 95% level of confidence. b.) Find a 90% level of confidence around the population variance. c.) Find a 90% level of confidence around the population standard deviation