The NDP propose a trial tax'iucrease program. Under this trial the socialinsuranoe numbers {SINs} of all supersrich Ontario residents are placed in a barrelI and a random sample of 12m of them is selected {assume there are a total of ll] super-rich Ontario residents) for taxation at the higher rate. The tax-inocme earned from this program will depend on the total income earned by the 1200 sampled residents. (note: that if the sample consisted of just two individuals1 with earnings of say $QUJH30 and $633,000 then the total income would be $1,530,\") The NDP recognise 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} [bl [2 points) Its expected value [c] [2 points) Its standard deviation [d) [4 points) Its interquartile range [IQH] Continuing on with the previous question. The Progremive Conservatives claim the average of 750 thousands per year [as the expected value for the earnings among Ontario super-rich) is an exaggeration, and have bet the NDP leader that the average annual earnings [per person) obtained from a sample of 120C] superrich will be less than 1'48 thousands per year. 4. Assume that the NDP assumptions (outlined in previous qnmtion] were correct. {a} [2 points) Will the NDP win this bet [yesfnm and why}? [In] [3 points) What is the probability that the NDP will win the bet? [c} [3 points) Would your answer to the previous question change if the sample size were doubled? How so {you should recalculate if you think it changes}. 3. Ontario politicians have recently discussed a proposal to raise the tax on Ontario res- idents who are labeled super-rich {earn $500 thousands per year or more in taxable income]. The NDP assume 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 fyr. (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? Briey explain your