The U.S. Census Bureau announced that the median sales price of new houses sold in 2011 was $227,200, and the mean sales price was $267,900 (www.census.gov/ new home sales, April 1, 2012). Assume that the standard deviation of the prices is $90,000.
a. If you select samples of n - 2, describe the shape of the sampling distribution of X.
b. If you select samples of n - 100, describe the shape of the sampling distribution of X.
c. If you select a random sample of n = 100, what is the probability that the sample mean will be less than $300,000?
d. If you select a random sample of n = 100, what is the probability that the sample mean will be between $275,000 and $290,000?