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7 .' Math3C - Sample Final Exam 2 8, (12 points) An organism has a lifetime X to be exponentially distributed with parameter .\ = 1 year. (a) Find the exact probability that the organism live more than 6 years. (b) Use Markov inequality to estimate this probability. (c) A more realistic model for its lifetime involves a hazard function .\(x) = 1 + eO,Ix. Estimate the probability that the organism live more than 6 years. 9. (10 points) To forecast the outcomes of a presidential election in which two candidates run for office, a telephone poll is conducted. 350 people are surveyed. The poll station claims that one candidate gets ,55% votes, and the result is accurate of 5% margih with a probability 95%. Can you confirm or disprove this claim? . 10. (12 points) A shipment contains 150 boxes and each box contains 50 oranges. Each orange has a probability 0.02 to be spoiled during the transport. (a) Use an appropriate approximation to determine the probability that a box contains no spoiled orange. (b) Find also an approximate answer to the probability that 30% of the boxes contains no spoiled orange.
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