A marketing firm takes a random sample of 12 households from its client's database. The client database lists the average annual household income for this random sample as the following: $85,000, $97,000, $76,500, $77,000, $99,000, $123,000, $68,000, $88,000, $111,000, $115,000, $90,000, $102,000.
a) Develop a 99% confidence interval for the population mean household income, assuming a normal distribution.
b) Create a normal probability plot for this data using PHStat (you do not need to submit the plot itself). Based on the plot, do you think it is reasonable to conclude that the data are normally distributed?