Question: The U.S. Census Bureau announced that the median sales price of new houses sold in January 2018 was $323,000, and the mean sales price was

The U.S. Census Bureau announced that the median sales price of new houses sold in January 2018 was $323,000, and the mean sales price was $382,700.
Assume that the standard deviation of the prices is $90,000.
a. If you select samples of n = 4, 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 $370,000?
d. If you select a random sample of n = 100, what is the probability that the sample mean will be between $350,000 and $365,000?

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