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1Module 5 Application Assignment – Probabilities, Estimation, and Confidence IntervalsInput your answers directly into this Word document. Do your own tabulations (without Minitab) for thisassignment when noted. Type your answers. Handwritten assignments will not be graded. All othercomputations complete with Minitab.Show appropriate output when using Minitab.1. The average annual cost of automobile insurance is $795 (National Association of InsuranceCommissioners, 2007). Use this value as the population mean and assume that the populationstandard deviation is σ=$100. Consider a sampling distribution with sample size of 50 automobileinsurance policies.Do not use Minitab and show all of your calculations.a.What is the standard error of the mean for the distribution of sample means of insurance costs?b.What is the probability that the sample mean is within $50 (between $745 and $845) of thepopulation mean?c. What is the sample mean insurance cost that is greater than 40% of the other mean insurancecosts?xd. Consider that you selected a random sample of 50 auto insurance policiesand find that thesample mean is $786. Assume the population standard deviation is the same as above (100).Calculate a 95% confidence interval for the true population mean cost of automobile insurance.Does the true population mean from above fall within this interval?
22. At a local car rental company, a sample of 200 callsfrom a customer service line was taken andfound that callers werekept waiting on average 12 minutes. The sample standard deviation is 4minutes.Do not use Minitab and show all of your calculations.a.Calculate a 90% confidence interval for the true population mean wait time for callers.