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. 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.

Review Binomial distribution Normal 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

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)

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?

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?

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?

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.