Please show ALL your works and round answers to 3 decimal places.

Replacement Costs: Transmissions You work for a consumer advocate agency and want to estimate the population mean cost of replacing a car's transmission. As part of your study, you randomly select 50 replacement costs and find the mean to be $2650.00. Assume the population standard deviation is $425.00. Construct a 95% condence interval for the population mean replacement cost. Interpret the results. #2 Determine a 90% confidence interval for the weekly time spent weight lifting given the data below: College Football The weekly time (in hours) spent weight lifting for 16 randomly selected college football players 7.4 5.8 7.3 7.0 8.9 9.4 8.3 9.3 6.9 7.5 9.0 5.8 5.5 8.6 9.3 3.8 Travel In a survey of 2230 US. adults, 1272 think that air travel is much more reliable than taking cruises. Construct a 95% confidence interval for the population proportion of US. adults who think that air travel is much more reliable than taking cruises. #4 Cholesterol Contents of Cheese A cheese processing company wants to estimate the mean cholesterol content of all one-ounce servings of cheese. The estimate must be within 0.5 milligram of the population mean. (a) Determine the minimum sample size required to construct a 95% confidence interval for the population mean. Assume the population standard deviation is 2.8 milligrams. (b) Repeat part (a) using a 99% confidence interval. (c) Which level of confidence requires a larger sample size? Explain. #5 SAT Scores The SAT scores of 12 randomly selected high school seniors 1700 1940 1510 2000 1430 1870 1990 1650 1820 1670 2210 1380 Find a 90% confidence interval for the mean SAT Score