The home ownership rate during 2009 declined to approximately 67% and is now comparable to the rate in early 2000 ( U.S. Census Bureau News, February 2, 2010).

A random sample of 80 households is taken from a small island community with 1,000 households. The home ownership rate on the island is equivalent to the national home ownership rate of 67%.

a. Calculate the expected value and the standard deviation for the sampling distribution of the sample proportion. Is it necessary to apply the finite population correction factor? Explain.

b. What is the probability that the sample proportion is within 0.02 of the population proportion? L056