According to the U.S. Statistical Abstract, the proportion of new single-family houses completed in 2003 that had exactly three bedrooms was 0.51. For samples of 30 new single-family houses completed in 2003, the distribution of sample proportion with exactly three bedrooms has mean 0.51, standard deviation 0.09, and a shape that is approximately normal.
a. The probability is 0.95 that sample proportion falls between what two values?
b. If a sample of 30 single-family houses completed in 2003 in a particular town has 0.70 with exactly three bedrooms, could we say that this sample represents what was typical for the United States?
c. What is the probability that sample proportion is less than 0.42 or greater than 0.60?