Chapter 7, Problem 8PS

The U.S. Census Bureau announced that the median sales price of new houses sold in 2016 was $\$316,500,$ and the mean sales price was $\$370,800$

Assume that the standard deviation of the prices is $\$90,000.$

a. If you select samples of $n=4,$ describe the shape of sampling distribution of $\text{<mover accent="true"> X <mo> ¯ </mo> </mover>}\text{.}$

b. if you select samples of $n=100,$ describe the shape of sampling distribution of $\text{<mover accent="true"> X <mo> ¯ </mo> </mover>}\text{.}$

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?