Ontario politicians have recently discussed a proposal to raise the tax on Ontario residents who are labeled super-rich (earn $500 thousand per year or more in taxable income). The NDP assumes that the probability model for the taxable earnings among the super-rich has an expected value of $690 thousand/yr and a standard deviation of $368 thousand/yr.

(a) (2 points) Consider the event that a randomly chosen person from the super-rich population has earnings in excess of $800,000/yr. How precisely can you determine the probability of this event? Briefly explain your answer.

The NDP proposes a trial tax-increase program. Under this proposal, a random sample of 1500 of them is selected (assume there are a total of 2200 super-rich Ontario residents) for taxation at the higher rate. The tax income earned from this program will depend on the total income earned by the 1500 sampled residents. (note: that if the sample consisted of just two individuals, with earnings of say $900,000 and $630,000 then the total income would be $1,530,000) The NDP recognizes that this total income is a random variable and have asked you to determine some summaries of this random variable as speced below. (state any assumptions when obtaining an answer)

(b) (2 points) Its expected value

(c) (2 points) Its standard deviation

(d) (4 points) Its inter-quartile range (IQR)