(Solved): A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of ...

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. Her realtor friend informs them that the last 25 houses that sold in their neighborhood took an average time of 200 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 50 days. (You may find it useful to reference the \( z \) table.) a. What assumption regarding the population is necessary for making an interval estimate for the population mean? Assume that the population has a normal distribution. Assume that the central limit theorem applies. b. Construct the \( 99 \% \) confidence interval for the mean sale time for all homes in the neighborhood. (Round final answer to 2 decimal places.)