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Problem 3. (P.6) In Chicago, complaints against police officers have led to a large amount of lawsuit settlements. These settlements are usually paid out of public city and county budgets. For officers involved in lawsuits, the amount of total settlement payouts per officer are distributed approximately normally with mean $50,000 and standard deviation $15,000. a) Officer Lastname has accounted for a total payout of $35,000. Find the z-score for this value. From this z-score and your knowledge of the Empirical Rule, what is the probability that a randomly selected officer accounts for a total payout of less than $35,000? Explain in detail how you know. Include a sketch of the normal distribution with this value marked, and the probability shaded. (b) Find the probability that a randomly selected officer that has been involved in a lawsuit accounts for over $100,000 of settlement payouts. Include a sketch of the normal distribution with the appropriate probability shaded. (c) Find a dollar amount x such that the probability of a randomly selected officer's total payout being less than x is equal to 0.05. Include a sketch of the normal distribution with the appropriate probability shaded. (d) Find a dollar amount a such that the probability of a randomly selected officer's total payout being greater than x is equal to 0.05. Include a sketch of the normal distribution with the appropriate probability shaded