10. Playbill magazine reported that the mean annual household income of its readers is $119,155 (Playbill, December 2003). Assume this estimate of the mean annual household income is based on a sample of 80 households and, based on past studies, the population standard deviation is known to be σ  $30,000.

a. Develop a 90% confidence interval estimate of the population mean.

b. Develop a 95% confidence interval estimate of the population mean.

c. Develop a 99% confidence interval estimate of the population mean.

d. Discuss what happens to the width of the confidence interval as the confidence level is increased. Does this result seem reasonable? Explain.