Instruction 8-9 A Wealthy Real Estate Investor Wants to Decide Whether It

Instruction 8-9
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.His 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.He 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.
-Referring to Instruction 8-9,if he 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?