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Construct the indicated confidence interval for the population mean u using the t-distribution. Assume the population is normally distributed. c= 0.90, x = 12.1, s= 0.92, n= 19 . . . (Round to one decimal place as needed.)You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals. A random sample of 60 home theater systems has a mean price of $150.00. Assume the population standard deviation is $15.80. . . . Construct a 90% confidence interval for the population mean. The 90% confidence interval is (,). (Round to two decimal places as needed.) Construct a 95% confidence interval for the population mean. The 95% confidence interval is (],). (Round to two decimal places as needed.) Interpret the results. Choose the correct answer below. O A. With 90% confidence, it can be said that the population mean price lies in the first interval. With 95% confidence, it can be said that the population mean price lies in the second interval. The 95% confidence interval is narrower than the 90%. O B. With 90% confidence, it can be said that the population mean price lies in the first interval. With 95% confidence, it can be said that the population mean price lies in the second interval. The 95% confidence interval is wider than the 90%. O C. With 90% confidence, it can be said that the sample mean price lies in the first interval. With 95% confidence, it can be said that the sample mean price lies in the second interval. The 95% confidence interval is wider than the 90%.Use the confidence interval to find the margin of error and the sample mean. (1.65, 1.91) (. . . The margin of error is (Round to two decimal places as needed.) The sample mean is (Type an integer or a decimal.)Use the confidence interval to find the margin of error and the sample mean. (0.642,0.740) . . . The margin of error is The sample mean isFind the margin of error for the given values of c, c, and n. c=0.90, o=2.7, n=81 5 Click the icon to view a table of common critical values. E = Cl (Round to three decimal places as needed.)