A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. They ask their Realtor friend for help and she informs them that the last 26 houses that sold in their neighborhood took an average time of 218 days to sell. The Realtor also tells them that based on her prior experience, the population standard deviation is 72 days.
a. What assumption regarding the population is necessary for making an interval estimate for the population mean?
b. Construct the 90% confidence interval for the mean sale time for all homes in the neighborhood.