A famly is relocating from St. Louis, Missourl, to Callomnla. Due to an increasing inwentory of houses in St. Louis, it is taking longer than betore to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market Her realsor friend informs them that the last 17 houses that sold in their neighborhocd took an average time of 245 days to sell. The realtor also tells them that bosed on her prior experience, the population standard deviation is 40 days. (You may find it useful to reference the z taig(e) a. Wrat assumption regarding the population is necessary for making an interval estimate for the population mean? Assume that the centrat Himit theorem applies. Assume that the population has a normal distribution. b. Construct the 99% confidence interval for the inean sale time for all homes in the neighborhood. (Round final answer to 2 decimal places.)