Realestate.com.au reports that the median property price in Randwick in September 2021 was $3,080,000 (https://www.realestate.com.au/neighbourhoods/randwick-2031-nsw). Suppose that the mean price was $4,000,000 and the standard deviation was $200,000.

a. If you take samples of size n=2, describe the sampling distribution of . Does this change if you take samples of size n=100? If so, describe the shape of the sampling distribution of .

b. If you take a random sample of size n=100, what is the probability that the sample mean will be less than $3,800,000?