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Chapter 9 Review Questions 1. The ACT has a mean of 18.6 and a standard deviation of 5.9. A group of 18 statistics students from the same class had a mean score of 21.8. a. What is the probability that a random sample of 18 would have a score this high (or higher)? b. Assuming that there is no cheating to explain the high scores, why is the mean not necessarily surprising? That is, how can a group have scores so far from the mean? 2. A basketball team averages 100.2 points per game during the 82 game season with a standard deviation of 9.7 points per game. During 17 games in the playoffs, they averaged 96.1 points per game. a. What is the probability that a group of 17 games randomly selected from the regular season schedule would have an average of at most 96.1 points? b. What is the probability that the team scores 410 points or more in 4 games? c. Are postseason games likely to represent a random sample of basketball games? Why or why not? 3. Suppose that a particular candidate for public office is favored by 48% of all registered voters in the district. A polling organization takes a random sample of 500 voters and will use p̂ , the sample proportion, to estimate p. a. What is the approximate probability that p̂ will be greater than .5, causing the polling organization to incorrectly predict the outcome of the upcoming election? b. Suppose the sample is increased to 750. Now what is the probability? c. If you wanted to limit this potential error to 5%, how large a sample size would you need? 4. A beverage company is suspected of underfilling its cans of soft drink. The company advertises that its cans contain, on average, 12 oz. of soda with s = .4 oz. a. Compute the probability that a random sample of 50 cans produces a mean fill of 11.9 oz. or less. b. Suppose each of 28 students in a statistics class collects a random sample of 50 cans and calculates the mean number of ounces of soda. Describe the sampling distribution for these 28 values of x . c. What important principle enabled us to answer the last question? Answers: 5.9 ) = .0107 ; b. The group is not an SRS. 18 9.7 410 9.7 2. a. normalcdf (0,96.1,100.2, ) = .0407 ; b. normalcdf ( ,1000,100.2, ) = .3177 ; c. The 4 17 4 competition tends to be stronger, the team is more experienced, etc., making these games different from the regular season, so not an SRS. 1. a. normalcdf (21.8,100,18.6, .48(.52) ) = .185 ; b. 500 .5 - .48 invNorm(.95) = 1.645 = s 1.645s = .02 3. a. normalcdf (.5,1,.48, normalcdf (.5,1,.48, .48(.52) ) = .136 ; c. 750 .02 .48(.52) = .01215 = 1.645 n .2496 .0001478 = n .2496 n= » 1689 .0001478 .4 .4 4. a. normalcdf (0,11.9,12, ) = .0385 ; b. N(12, ) = N(12,.0566) ; c. Central Limit 50 50 Theorem s=