me to solve this equation Subject : Stats and Prob 1.) A population has mean = 227.6 = 227.6 and = 20.4 = 20.4 . You intend to draw a random sample of size n = 101 n = 101 . (a) What is the shape of the sampling distribution of means? right-skewed bimodal normal uniform left-skewed (b) What is the center of the sampling distribution of means? x = x = Round to four decimal places as needed. (c) What is the standard error of the sampling distribution of means? x = x = Round to four decimal places as needed. 2.) A population of values has an unknown distribution with = 173.2 = 173.2 and = 55.1 = 55.1 . You intend to draw a random sample of size n = 80 n = 80 . What is the mean of the distribution of sample means? x = x = (Please enter an exact answer.) What is the standard deviation of the distribution of sample means? x = x = (Please report your answer accurate to 2 decimal places.) 3.) You want to obtain a sample to estimate a population mean age. Based on previous evidence, you believe the population standard deviation is approximately =15.9 years. You would like to be 99% confident that your estimate is within 10 years of the true population mean. How large of a sample size is required? Give the minimum size that will work. n = 4.) You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately = 32.7 = 32.7 . You would like to be 90% confident that your esimate is within 1.5 of the true population mean. How large of a sample size is required? n = Do not round mid-calculation. However, use a critical value accurate to three decimal places this is important for the system to be able to give hints for incorrect answers. 5.)A political candidate has asked you to conduct a poll to determine what percentage of people support her. If the candidate only wants a 5% margin of error at a 95% confidence level, what size of sample is needed? Give your answer in whole people. 6.)You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately = 66.5 = 66.5 . You would like to be 90% confident that your estimate is within 0.5 of the true population mean. How large of a sample size is required? [Do not round mid-calculation. However, use a critical value rounded to three decimal places this is important for the system to check answers correctly.] n = 7.) You measure 31 watermelons' weights, and find they have a mean weight of 59 ounces. Assume the population standard deviation is 12.3 ounces. Based on this, what is the maximal margin of error associated with a 95% confidence interval for the true population mean watermelon weight. Give your answer as a decimal, to two places ounces 8.) What is the critical value, t, for a 95% confidence interval with a sample size of 7? 2.365 1.943 2.447 1.895 9.) You measure 45 watermelons' weights, and find they have a mean weight of 45 ounces. Assume the population standard deviation is 9.4 ounces. Based on this, construct a 95% confidence interval for the true population mean watermelon weight. Give your answers as decimals, to two places ounces 10.) In 2011 the U.S. Department of Transportation reported with 95% confidence that the average length of a motor vehicle trip in the United States was 9.72 miles with a margin or error of 0.22 miles. With 95% confidence the authors of the report are claiming that the true average length of a motor vehicle trip in the United States is between and miles. The level of confidence for this estimate is %