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### Homework 3

Course: STAT 111, Fall 2008
School: UPenn
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Word Count: 639

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111 Statistics Summer 2008 Homework 3 Due: Monday, June 16 Questions from the book: 1. 2. 3. 4. 5. 6. 7. 8. 9. Question 4.116 (Academic degrees and gender) pg 305 Question 4.130 (Toss a pair of dice two times) pg 307 Question 4.132 (Some probability distributions) pg 307 Question 1.126 (Compare an SAT score with an ACT score) pg 74 Question 1.139 (Length of pregnancies) pg 75 Question 5.54 (Flaws in carpets) pg...

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111 Statistics Summer 2008 Homework 3 Due: Monday, June 16 Questions from the book: 1. 2. 3. 4. 5. 6. 7. 8. 9. Question 4.116 (Academic degrees and gender) pg 305 Question 4.130 (Toss a pair of dice two times) pg 307 Question 4.132 (Some probability distributions) pg 307 Question 1.126 (Compare an SAT score with an ACT score) pg 74 Question 1.139 (Length of pregnancies) pg 75 Question 5.54 (Flaws in carpets) pg 349 Question 5.56 (Risks and insurance) pg 349 Question 5.48 (ACT scores of high school seniors) pg 347 Question 5.70 (Genetics of peas) pg 351 More Questions (required): 10. Jules, Vincent, and Mia are physicians at the local hospital. One of their duties is being on call during non-working hours to handle any emergencies that might come up. Each carries a pager that can be activated by hospital personnel. Suppose Jules responds to his pager 60% of the time, Vincent responds to his pager 45% of the time, and Mia responds to her pager 65% of the time. If each person responds independently, what is the probability that at least one of them could be contacted in the event of an emergency? 11. A die is loaded in such a way that the probability of any particular faces showing is directly proportional to the number on that face. What is the probability that an even number appears when the die is tossed? 12. Laboratory data show that the time required to complete two chemical reactions in a production process varies. The first reaction has a mean time of 35 minutes and a standard deviation of 1.5 minutes; the second has a mean time of 20 minutes and a standard deviation of 1.2 minute. The two reactions are run in sequence during production. There is a fixed period of 4.5 minutes between them as the product of the first reaction is pumped into the vessel where the second reaction will take place. a) What is the mean time required for the entire process? b) Assuming the two reactions are independent, what is the standard of deviation the time required for the entire process? (Be careful. This is a hard question.) 13. Scores on a typical IQ test follow approximately a normal distribution with mean of 100 and SD of 17. a) What percent of the people taking the test score below 100? What percent of the people taking the test score between 90 and 110? b) Ginger takes the test and scores in the top 15% of all people taking the test. What was her minimum test score? 14. Say we have a random variables X, where X has a normal distribution with a mean of 0 and a standard deviation of 10. Of the two probabilities P(1 < X < 1) and P(1 < X < 3), which is larger? Explain briefly (no calculation is necessary). Drawing a picture may be easiest. 15. Say we have two random variables X and Y, both of which have a normal distribution with a mean of 0. However, X has a SD of 10 while Y has a SD of 5. Of the two probabilities P(1 < X < 1) and P(1 < Y < 1), which is larger? Explain briefly (no calculation is necessary). 16. Is it more likely to observe eight or more heads in ten flips of a fair coin or to observe 16 heads or more in twenty flips? 17. In 1973, Charles Tar...

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