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Final Review Part B

Final Review Part B - 1 Thelifespan ofa qu een antfollowsth...

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MATH 218 SI Final Review (Spring 2009) Part B 1. The lifespan of a queen ant follows the following distribution: ‐(4/5)x+1 0≤x<1 f(x) = c 1≤x≤3 0 x<0, x>3 (a) Find the function f(x)=c that is distributed 1 ≤ x ≤ 3 (note: c is a constant). (b) What is the average lifespan of a queen ant? (c) If after one year, the queen ant is still alive, what is the probability it will still be alive for at least another five months? (d) When one queen ant dies, another queen ant immediately takes its place, as any given ant hill will always be ruled by a queen ant. If an ant hill goes through 30 different queen ants, what is the probability that this ant hill is at least 28 years and four months old?
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2. Slick Motor Tire Inc. uses a tire mold which occasionally, and randomly, produces out‐of‐round tires. In fact 20% of the tires which it produces are out‐of‐round. Suppose Slick takes a random sample of 10 tires produced by this tire mold. (a) Find the expected number of out‐of‐round tires among these 10. (b) Find the probability that two or more of these 10 tires are out‐of‐round. (c) Suppose now that the Fraud Motor Company buys 120 of the tires produced by this tire mold. Find the approximate probability that between 20 and 30 (inclusive) of these tires are out‐of‐round. 3. John regularly plays a target shooting competition in his yard. He is not very good at the game and his score has the following probability distribution Score 0 1 2 3 Prob. 0 . 1 0 . 4 0 . 3 0 . 2 (a) Find the expected value and standard deviation of John’s score. (b) Suppose he plays the game twice. Find the probability that his total is at least 5. (c) Suppose he plays the game 50 times. Find the probability that his total is at least 75.
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4. Happy Hungry Hamburger restaurant cooks an average of 1800 hamburgers patties a week, with a standard deviation of 200 hamburger patties. Assume that the number of hamburger patties grilled follows a normal
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