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 50 home theater systems has a mean price of ​$128.00. 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.