A Housing Developer Suspects That Housing Prices in a Geographical $\$ 64,000$

Short Answer

A housing developer suspects that housing prices in a geographical area are higher than the national average. Suppose the average national home price is $\$ 64,000$ with a standard deviation of $\$ 5,000$ , and the developer decides to build the community only if, in a random sample of 50 newly -sold houses, the average price is more than $\$ 66,000$ .
-What is the probability that the developer builds the community when the prices in the area are only average?