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Stat 245 Recitation 12

Stat 245 Recitation 12. 10/30/2007 EA 285 10:30am TA: Dongmei Li. Announcement. I can add 2 points to your Exam 1 if you marked “F” on True/False question No.9 in version A and question No.10 in version B.

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Stat 245 Recitation 12

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  1. Stat 245 Recitation 12 10/30/2007 EA 285 10:30am TA: Dongmei Li

  2. Announcement • I can add 2 points to your Exam 1 if you marked “F” on True/False question No.9 in version A and question No.10 in version B. • Homework 7 is due on Friday (Nov.2) in lecture. It include following questions from chapter 7: 7.74, 7.76, 7.80, 7.102, 7.104, 7.112, and 7.120.

  3. Review • Binomial distribution • Page 388 shaded area in textbook • Page 390 shaded area (how to use appendix table 9 to find the binomial distribution) • When X is sampled without replacement, sample size n/ Population size N ≤ 0.05, binomial distribution gives a good approximation to the probability distribution of X. • Normal distribution • Page 399 and 400 shaded area in textbook • Normal approximation to a Binomial Distribution • When n π ≥ 10 and n (1-π) ≥ 10, can use normal approximation. • Page 427 shaded area in textbook

  4. Problem solving--- Chapter 7 • 7.60 Suppose that 90% of all registered California voters favor banning the release of information from exit polls in presidential elections until after the polls in California close. A random sample of 25 California voters is to be selected. • a. What is the probability that more than 20 voters favor the ban? • b. What is the probability that at least 20 voters favor the ban? • c. What are the mean value and standard deviation of the number of voters who favor the ban? • d. If fewer than 20 voters in the sample favor the ban, is this at odds with the assertion that (at least) 90% of the populace favors the ban? (Hint: Consider P(X<20) when π=.90)

  5. Problem solving--- Chapter 7 • 7.77 The time that it takes a randomly selected job applicant to perform a certain task has a distribution that can be approximated by a normal distribution with a mean value of 120 sec and a standard deviation of 20 sec. The fastest 10% are to be given advanced training. What task times qualify individuals for such training?

  6. Problem solving--- Chapter 7 • 7.107 A pizza company advertises that it puts 0.5 lb of real mozzarella cheese on its medium pizzas. In fact, the amount of cheese on a randomly selected medium pizza is normally distributed with a mean value of 0.5 lb and a standard deviation of 0.025lb. • a. What is the probability that the amount of cheese on a medium pizza is between 0.525 and 0.550lb? • b. What is the probability that the amount of cheese on a medium pizza exceeds the mean value by more than 2 standard deviations? • c. What is the probability that three randomly selected medium pizzas all have at least 0.475 lb of cheese?

  7. Problem solving--- Chapter 7 • 7.122 The lightbulbs used to provide exterior lighting for a large office building have an average lifetime of 700 hr. If length of life is approximately normally distributed with a standard deviation of 50 hr, how often should all the bulbs be replaced so that no more than 20% of the bulbs will have already burned out?

  8. Problem solving--- Chapter 7 • 7.123 Suppose that 16% of all drivers in a certain city are uninsured. Consider a random sample of 200 drivers. • a. What is the mean value and standard deviation of the number who are uninsured? • b. What is the (approximate) probability distribution that between 25 and 40 (inclusive) drivers in the sample were uninsured? • c. If you learned that more than 50 among the 200 drivers were uninsured, would you doubt the 16% figure? Explain.

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