36. Casinos. Governor Deval Patrick of Massachusetts proposed legalizing casinos in Massachusetts although they are not currently legal, and he included the revenue from them in his latest state budget. The website www.boston

.com conducted an Internet poll on the question: “Do you agree with the casino plan the governor is expected to unveil?”

As of the end of 2007, there were 8663 votes cast, of which 63.5% of respondents said: “No. Raising revenues by allowing gambling is shortsighted.”

a) Find a 95% confidence interval for the proportion of voters in Massachusetts who would respond this way.

b) Are the assumptions and conditions satisfied? Explain.