(8) 6. Refrigerators last on average 19.65 years with a standard deviation of 3.1 years (time they last is normally distributed). a) Find the probability a refrigerator you just bought will last more than 23 years? Show work b) A refrigerator company plans to offer a warranty on the refrigerators they manufacture (the warranty states the company will replace the fridge for free if it does not last a certain amount of time) . They wish to offer the warranty so that they only have to replace 1.13% of all the refrigerators they make. How long should they make the warranty for? Show work (9) 7. A state has a scratch off lottery game in which they print 1,000,000 tickets. 975,000 of the tickets are losers meaning they have no cash value. The state makes 24,500 of the tickets worth $2, then 400 tickets worth $100, 99 tickets worth $1,000 and 1 ticket worth $100,000. a) Write out the probability distribution for the random variable x where x is the cash value of the ticket b) Find the average value for x c) Interpret the answer you get for b)