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An insurance company offers Insurance for broken cell phone screens over the life of the cell phone. A repair of a screen costs the company $100. Suppose the probability that an individual breaks their screen is 20%. Further suppose that individuals either break their screen exactly zero times or exactly one time over the life of their cell phone (this is of course unrealistic). The insurance company's profit in dollars from insured individual is therefore n=P-1005 where P is the premium (price) charged the individual up front and Sy is the Indicator random variable that is 1 if the individual's screen breaks (which happens with 20% probability), and otherwise. We will assume that the premium P must be the same for all individuals insured, and therefore P is just a constant (and not random). Profit per insured individual when the company insures n Individuals is a random variable which we can write as 3 TES 11. Suppose the insurance company charges $20 to each insured individual (so P = 20), and that the insurance company insures 10000 individuals. What is the approximate probability that the insurance company has a negative profit per insured individual, Le. what is the chance the company loses money? (Use the central limit theorem) a) 76.3% b) 50.0% c) Less than 15 d) 10.656 e) 20.4% 12. Now suppose the insurance company instead charges $20.50 to each insured individual, and that the insurance company again insures 10000 individuals. What is the approximate probability that the Insurance company loses money? (Use the central limit theorem) a) 76.3% b) 50.0% c) Less than 194 d) 10.6%

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