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Question 2 The Body Mass Index (BMI) is a value calculated based on the weight and the height of an individual. In a small European city, a survey was conducted one year ago to review the BMI of the citizens. In the sample with 200 citizens, the mean BMI was 23.3 kg/m and standard deviation was 1.5 kg/m. It is reasonable to assume the BMI distribution is a normal distribution. (a) Find the point estimate of the population mean BMI one year ago. (b) Calculate the sampling error at 90% confidence. (c) Construct a 90% confidence interval estimate of the population mean BMI one year ago. This city launched a healthy exercise program to reduce citizen's BMI after last year's survey. Suppose the program effectively reduces the BMI of each citizen by 2.5%. (d) Construct a 98% confidence interval estimate of the population mean BMI after the healthy exercise program. (Hint: find the updated sample mean and sample standard deviation of the BMI of the sample with 200 citizens selected last year)