Scenario 1


Imagine that the per person income for a large city is normally distributed and that a particular randomly selected person has an income that is 1.3 standard deviations above the mean.



(a) What is the probability that a second random sample will produce a person whose income is less than the first?

(b) What about more than the first?

(c) What is the probability that a second random sample produces a person whose income is more extreme (further from the mean) than the first?

(d) What about less extreme (closer to the mean)?

(e) What role does regression to the mean play in this problem?



Hint: You may find the following online zscore/probability calculator helpful: https://davidmlane.com/hyperstat/z_table.html