In a sample of 150 residents, each person was asked if he or she favored the concept of having a single, countywide police agency. The county is composed of one large city and many suburban townships. The residence (city or outside the city) and the responses of the residents are summarized in the following table. (Enter your probabilities as fractions.) Residence Favor Oppose Total In the city 60 50 ' 110 Outside the city 25 15 40 Total 150 (a) What is the probability that a randomly selected individual from this group of respondents is in favor of the concept of having a single, countywide police agency? (b) Calculate the probability. The probability that a randomly selected individual from this group of respondents lives in the city is If you roll a pair of fair dice, what is the probability of getting the following sums? (Enter your probabilities as fractions.) (a) a sum of 1 (b) a sum of 4 (c) a sum of 12 Complete the following sentence. The ---Select--- 3 of two events E and F is denoted by E U F. 6. [I1 Points] DETAILS STATSQC1 7.1G.001. Complete the following sentence. The ---Select--- 3 of two events E and F is denoted by E n F. Educators wish to look at IQ scores of elementary students from a very large school district. (a) First, the educators take a small random sample of seven students and administer IQ tests. The following are the test scores. 92, 99, 90, 103, 119, 108, 115 Find the mean IQ score of these seven students. (Round your answer to one decimal place.) (b) Find the median IQ score of these seven students. (c) Now the educators want more information, so they gather data on the following. S = event student has a sibling L = event student lives with a single parent The data collected suggest the following. p($) = 0.77 P(L) = 0.23 .05 n L) = 0.15 Find the probability of the union of the events "student has a sibling" and "student lives with a single parent." Bernie the Gambler is betting on several games this month. He can bet that one team will win, the other team will win, or that there will be a tie. The probabilities of each team winning or a tie are given in the table below. Team Atoms Generals Atoms Win: 0.30 Generals Win: 0.08 Eagles Eagles Win: 0.60 Eagles Win: 0.85 Tie: 0.10 Tie: Generals Win: 0.24 Atoms Atoms Win: 0.73 Tie: 0.03 (a) For the Eagles versus Atoms game, if Bernie bets on both teams in the same game, then the events "Eagles win" and "Atoms win" are which of the following? mutually exclusive independent " neither mutually exclusive nor independent both mutually exclusive and independent (b) what is the probability of a tie between the Eagles and the Generals? (c) Bernie decides to go with the long odds and bet on the teams that are the underdogs. What is the probability that the Generals will beat both the Eagles and the Atoms and that the Atoms will beat the Eagles? (Assume each game is independent.) Q and R are independent events. P(Q) = 0.4; P(Q AND R) = 0.12. Find P(R). P(R) = Additional Materials [I] Reading [-13 Points] DETAILS DIEZSTAT4 3.1.005. If you flip a fair coin 12 times, what is the probability of getting the following? (Enter your probabilities as fractions.) (a) all tails (b) all heads (c) at least one tails Each year, a manufacturing and information rm surveys new car owners 90 days after they have purchased their cars. The data collected are used to rate auto brands (such as Audi, Ford, Jaguar, etc.) on initial quality and customer satisfaction. Initial quality is measured, in part, on the number of manufacturing defects per 100 vehicles. Suppose that in a recent survey, 11% of those surveyed reported having a defect in his or her new car. (a) Calculate the probability. The probability that a randomly selected individual from those surveyed did not report that his or her car had a defect in the rst 90 days is (b) Is the response to the question "Did your car have a defect within the first 90 days of owning it?" categorical, numerical, or neither? ' categorical ' numerical ' neither A survey estimates that 14.9% of Americans live below the poverty line, 20.8% speak a language other than English (foreign language) at home, and 4.9% fall into both categories. (a) Are living below the poverty line and speaking a foreign language at home disjoint? 0 Yes, because no one is both living below the poverty line and speaking a language other than English at home. ' No, because there are people living below the poverty line and speaking a language other than English at home. (b) Draw a Venn diagram summarizing the variables and their associated probabilities. (Enter your answers to three decimal places.) speak foreign language below poverty line (D (c) What percent of Americans live below the poverty line and only speak English at home? (Enter your answer to one decimal place.) 0/0 (d) What percent of Americans live below the poverty line or speak a foreign language at home? (Enter your answer to one decimal place.) % (e) what percent of Americans live above the poverty line and only speak English at home? (Enter your answer to one decimal place.) % (f) 15 the event that someone lives below the poverty line independent of the event that the person speaks a foreign language at home? (Enter your answers to four decimal places.) Using the multiplication rule, P(below poverty line) x P(speak foreign language) = %, while P(below poverty line and speak foreign language) = %. Since these two values are ---Select--- , the events are ---Se|ect--- a