A wealthy real estate investor wants to decide whether it is a good investment to build a high-end shopping complex in a suburb of Sydney. The investor's main concern is the total market value of the 3,605 houses in the suburb. From past experience, the standard deviation of market housing prices is estimated to be $81,000. The investor commissioned a statistical consulting group to take a sample of 200 houses and obtained a sample average market price of $450,000 and a sample standard deviation of $77,400. The consulting group also found out that the average differences between market prices and appraised prices was $250,000 with a standard deviation of $6,800. Also, the proportion of houses in the sample that are appraised for higher than the market prices is 0.24.

What will be the 90% confidence interval for the average market price of the houses in the suburb constructed by the consulting group?

What will be the 90% confidence interval for the population proportion of houses that will be appraised for higher than the market prices?

If the investor wants a 95% confidence on estimating the true population average market price of the houses in the suburb to be within $20,000, how large a sample will he need?