Part a) What is the expected number of policies that will pay out before the insured parties have reached age 61? 0.5 Part b) What is the variance of the number of policies that will pay out before the insured parties have reached age 61? 0.475 Part c) What is the probability that at least two policies will pay out before the insured parties have reached age 61?

6.  An expert witness for a paternity lawsuit testifies that the length of a pregnancy is normally distributed with a mean of 280 days and a standard deviation of 13 days. An alleged father was out of the country from 240 to 306 days before the birth of the child, so the pregnancy would have been less than 240 days or more than 306 days long if he was the father. The birth was uncomplicated, and the child needed no medical intervention. What is the probability that he was NOT the father? What is the probability that he could be the father?

For 10 percent of the products in a category, a firm fails to satisfy all demand during themonth. What is its in-stock probability?

The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 15.7% daily failure rate. Complete parts (a) through (d) below. a. What is the probability that the student's alarm clock will not work on the morning of an important final exam? | (Round to three decimal places as needed.) b. If the student has two such alarm clocks, what is the probability that they both fail on the morning of an important final exam? (Round to five decimal places as needed.) c. What is the probability of not being awakened if the student uses three independent alarm clocks? (Round to five decimal places as needed.) d. Do the second and third alarm clocks result in greatly improved reliability? O A. No, because total malfunction would still not be unlikely. O B. No, because the malfunction of both is equally or more likely than the malfunction of one. OC. Yes, because you can always be certain that at least one…

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2. If an insurance company issues a $200,000 five-year policy on a man whose probability of living for another five years is .994, what is the minimum that the expected cost to the company for this policy?