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Mario11ab_Spring08

Mario11ab_Spring08 - MATH 218 SI Session(Spring 2008 SI...

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Unformatted text preview: MATH 218 SI Session (Spring 2008) SI Leader: Mario Week 11 Worksheet Wednesday (3/26) Professor: Zygouras/Dumett www.usc.edu/si 1. Raz and Zar are both running for the position of President of Stuffed Animal Kingdom. To win, a candidate must receive more than 50% of the votes. In a pre-election survey of 200 citizens of Stuffed Animal Kingdom. 120 supported Raz while 80 supported Zar. a. Can you conclude with 98% confidence that Raz will be the winner? b. How many more samples would you have to take if you would like the width of 98% confidence interval to be 10%? c. Repeat part “b” if you did not know p-hat from the preliminary sample. 2. At Trojan Lake, the new fishing season has arrived. The weights of fish in this lake are normally distributed with a mean of 3 pounds and a standard deviation of 0.75 pounds. a. A sample of 16 fish is caught. Find the probability that the average weight of a fish is at most 2.9 lbs. b. From a sample of 16 different fish, find the probability that this batch of fish will weight more than 50 lbs. 3. Zygouras Muffin Factory produces a variety of muffins for the staff and students of USC. 25% of the muffins produced are chocolate chip, 15% are oatmeal, 20% are blueberry, and 40% are plain. a. The math department secretary orders 500 muffins (for Math 218 students) without specifying what type she wants. If the muffins are packed at random, what is the probability that there will be exactly 100 blueberry muffins? b. What is the probability that there will be anywhere between 98 and 102 blueberry muffins? c. What is the probability that at least 26% of the muffins that arrive are chocolate chip? d. What is the probability that at most 41% of the muffins are plain? 4. Zygouras Accounting Company has 3% of its employees who have attended graduate school. In Department A of the company, there are 500 employees. a. Find the probability that the proportion of employees in this department who have attended graduate school is less than 4%. b. In Department B, there are a total of 250 employees. Find the probability that between 4 and 8 (all inclusive) employees from this department have attended graduate school. c. In Department B, find the probability that exactly 20 of them have attended graduate school. 5. A random sample of 100 Kit Kat Bars is taken and weighted. The sample mean is 41.6 grams and the population standard deviation is 1.5 grams. a. Construct the 95% confidence interval for μ . b. Construct the 99% confidence interval for μ . 6. The student attendance at USC football games follows a normal distribution. In a sample of 9 games, the attendance rates are: 8,000 7,600 8,400 6,120 9,200 7,800 9,400 6,200 8,200 a. Calculate the point estimator for μ , the population mean....
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Mario11ab_Spring08 - MATH 218 SI Session(Spring 2008 SI...

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