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4. Suppose that 30% of the population has type A blood.
- (a)If 8 people are selected at random, what is the probability that at least four of them have type A blood.
- (b)If 80 donors come to give blood one day, what is the probability that at least forty of them have Type A blood (using the normal approximation)? Explain why this is higher or lower than the answer in part (a).
- (c) If 20 people come to give blood, what is the probability that at least one of the donors is of Type A? (I’d be impressed if you could solve this in two different ways. . . )
4. An airline knows that the mean weight of all pieces of passengers’ luggage is 49.3 lb with a standard deviation of 8.4 lb. What is the probability that the weight of 66 bags in a cargo hold is more than the plane’s total weight capacity of 3,500 lb?
5. The Federal Reserve reports that the mean lifespan of a five dollar bill is 4.9 years. Let’s suppose that the standard deviation is 1.7 years and that the distribution of lifespans is normal (not unreasonable!)
Find: (a) the probability that a $5 bill will last less than 3 years.
(b) the probability that a $5 bill will last between 5 and 8 years.
(c) the 2nd percentile for the lifespan of these bills (a time such that 2% of bills last less than that time).
(d ) the probability that a random sample of 32 bills has a mean lifespan of more than 5.2 years.
6. A health insurance company charges policyholders a $1350 annual premium for health insurance for hospitalization. The company estimates that each time a patient is hospitalized costs the company $2500. Furthermore, they have estimated that 85% of patients will not be hospitalized, 10% will be hospitalized once a year, and no one will be hospitalized more than twice.
(a) Find the insurance company’s expected profit per policyholder.
(b) What is the expected profit if they enroll 80,000 policyholders?