Problem 4 Marital Status The probability that a randomly chosen 65-yearold woman is divorced is about 0.14. This probability is a long-run proportion based on all the millions of women aged 65. Let's suppose that the proportion stays at 0.14 for the next 45 years. Bridget is now 20 years old and is not married. Bridget thinks her own chances of being divorced at age 65 are about 5%. Explain why this is a personal probability. Select all of the statements that are true: C] This probability is the long-run behavior for 100 women, 5 of whom were divorced before age 65. C] This probability represents the proportion of Bridget's female relatives who got divorced before age 65. C] Since a woman is either divorced or is not divorced, the probability of either of these events is 5%. C] This is based on a personal judgment of her likelihood to get divorced; it is not based on data on repeated trials of an experiment. QUESTION 3 Problem 5 Personal Probability? When there are few data, we often fall back on personal probability. There had been just 24 space shuttle launches, all successful, before the Challenger disaster in January 1986. The shuttle program management thought the chances of such a failure were only 1 in 100,000. Suppose 1 in 100,000 is a correct estimate of the chance of such a failure. If a shuttle was launched every day, about how many failures would one expect in 300 years? [a] (Round to the nearest integer.) QUESTION 4 Problem 7 An Eerie Coincidence? An October 6, 2002, ABC News article reported that the winning New York State lottery numbers on the one-year anniversary of the attacks on America were 911. Should this fact surprise you? Explain your answer. O This is could not have happened by chance. The lottery must have been rigged that day. O This is highly unlikely. Lottery numbers are randomly selected numbers. Q There are 1000 distinct three-digit numbers, from 000 to 999. Each of these numbers is equally likely (probability 0.001). While it is unlikely for the New York State lottery numbers to match on the one-year anniversary of the attacks on America, it is not impossible. O This is not a surprising outcome. Every once in a while the winning lottery number is the date the number was drawn. ' ........ Problem 8 In the Long Run The probability of a head in tossing a coin is 1/2. This means that as we make more tosses, the proportion of heads will eventually get Close to 0.5. It does not mean that the count of heads will get close to 1/2 the number of tosses. To see why, imagine that the proportion of heads is 0.49 in 100 tosses, 0.493 in 1000 tosses, 0.4969 in 10,000 tosses, and 0.49926 in 100,000 tosses of a coin. How many heads came up in each set of tosses? How close is the number of heads to half the number of tosses? - v 0.49 in 100 tosses A. 49.926 heads V 0.493 in 1,000 tosses B. 49 heads c, 493 heads - v 0.4969 in10,000 tosses - v 0.49926 in 100,000 tosses 04.969 heads AI Il-rv-I-Ill :- A couple plan to have three children. List the possible arrangements of girls and boys. For example, GGB means the first two children are girls and the third child is a boy. All arrangements are (approximately) equally likely. Select the correct answer for each problem below. - v The number of possible arrangements is A. 4 - v The possible arrangements are 3 BBB= 886, I368, EGG! GBB, GBG: GGB' GGG - v The probability of each of the arrangements is C' 1'4 - v The probability that couple has 2 girls and one boy is D' 8 E. BBB, GGG, BBG, GGB F. 1/8 (5, 3/8 QUESTION 9 Question 22 Applying to College You ask an SRS of 1500 college students whether they applied for admission to any other college. Suppose that in fact 35% of all college students applied to colleges besides the one they are attending. (That's close to the truth.) The sampling distribution of the proportion of your sample who say \"Yes\" is approximately Normal with mean 0.35 and standard deviation 0.01. Choose the best answer for each problem below. Answers may be use once, more than once or not at all. _ v What percentage of many samples would have a A. 5% sample proportion less than .335? Use z-score B 10% (standard score) to nd this answer. ' c, 6.68% - v What percentage of many samples would D 10/ . 0 have a sample proportion larger than 0.37? (Use the 689599] rule.) E. 2.5% _ v What is the probability that your sample will have a F- '15 proportion less than 0.33? _ v Use Rule D: what is the probability that your sample result will be either less than 0.33 or greater than 0.37? 15. High school academic rank. Select a rst-year college student at random and ask what his or her academic rank was in high school. Here are the probabilities, based on proportions from a large sample survey of rst- year students: Rank: Top 20% Second 20% Third 20% Fourth 20% Lowest 20% Probability: 0.44 0.26 0.23 0.06 0.01 HUEDI IUI' I Question 15 High School Academic Rank The probability that a randomly chosen rstyear college student was not in the top 20% of his or her high school class is The probability that a first-year student was in the top 40% in high school is 3. Winning a baseball game. Over the period from 1965 to 2011 the champions of baseball's two major leagues won 63% of their home games during the regular season. At the end of each season, the two league champions meet in the baseball World Series. Would you use the results from the regular season to assign probability 0.63 to the event that the home team wins a World Series game? Explain your answer. Problem 3 Winning a Baseball Game You should use the results of the regular season to assign probability 0.63 to the event that the home team wins the World Series. 0 True 0 False 13. Our next president? A Gallup Poll on Presidents Day 2008 interviewed a random sample of 1007 adult Americans. Those in the sample were asked which former president they would like to bring back as the next president if they could. Here are the results: Outcome Probability John F. Kennedy 0.23 Ronald Reagan 0.22 Abraham Lincoln 0.10 Someone else ? \\(uLzlluli u Problem 13 Our Next President? The probability that the person chosen selects someone other than John F. Kennedy, Ronald Reagan, or Abraham Lincoln is The event \"I would select either John F. Kennedy or Ronald Reagan\" contains the rst two outcomes. The probability of this event is