[Source: CBS SportsLine.com, www.sportsline .com.]
a. Approximate the mean and standard deviation of the batting averages from the histogram.
b. Compare the distributions of batting averages for the two leagues. (See E94 for the American League.) What are the main differences between the two distributions?
c. A batter hitting .300 in the National League is traded to a team in the American League. What batting average could be expected of him in his new league if he maintains about the same position in the distribution relative to his peers?
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AP1. These summary statistics are for the distribution of the populations of the major cities in Brazil.
Which of the following best describes the shape of this distribution?
skewed right without outliers skewed right with at least one outlier roughly normal, without outliers skewed left without outliers skewed left with at least one outlier AP2. Which of these lists contains only summary
statistics that are sensitive to outliers? mean, median, and mode
standard deviation, IQR, and range mean and standard deviation median and IQR
five-number summary
AP3. This stem-and-leaf plot shows the ages of CEOs of 60 corporations whose annual sales were between $5 million and $350 million. Which of the following is not a correct statement about this distribution?
The distribution is skewed left (towards smaller numbers).
The oldest of the 60 CEOs is 74 years old. The distribution has no outliers.
The range of the distribution is 42. The median of the distribution is 50.
AP4. A traveler visits Europe and stays thirty days in thirty different hotels, paying each
day with her credit card. The hotels charged a mean price of 50 euros, with a standard deviation of 10 euros. When the charges appear on her credit card statement in the United States, she finds that her bank charged her $1.20 per euro, plus a $5 fee for each transaction. What is the mean and standard deviation of the thirty daily hotel charges in dollars, including the fee?
mean $50, standard deviation $17 mean $60, standard deviation $12 mean $60, standard deviation $17 mean $65, standard deviation $12 mean $65, standard deviation $17 AP5. The scores on a nationally administered test
are approximately normally distributed with mean 47.3 and standard deviation 17.3. Approximately what must a student have scored to be in the 95th percentile nationally?
AP6. A particular brand of cereal boxes is labeled “16 oz.” This dot plot shows the actual weights of 100 randomly selected boxes. Which of the following is the best estimate of the standard deviation of these weights?
AP7. The distribution of the number of points earned by the thousands of contestants in the Game of Pig World Championship has mean 20 and standard deviation 6. What proportion of the contestants earned more than 26 points?
102
Chapter 2 Exploring Distributions
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Less than 1% 16%
32% 84%
This proportion cannot be determined from the information given.
AP8. Anya scored 70 on a statistics test for which the mean was 60 and the standard deviation was 10. She also scored 60 on a chemistry test for which the mean was 50 and the standard deviation was 5. If the scores for both tests were approximately normally distributed, which best describes how Anya did relative to her classmates?
Anya did better on the statistics test than she did on the chemistry test because she scored 10 points higher on the statistics test than on the chemistry test.
Anya did equally well relative to her classmates on each test, because she scored 10 points above the mean on each. Anya did better on the chemistry test than she did on the statistics test because she scored 2 standard deviations above the mean on the chemistry test and only 1 standard deviation above the mean on the statistics test.
It’s impossible to tell without knowing the number of points possible on each test. It’s impossible to tell without knowing the number of students in each class.
Investigative Task
AP9. A game invented by three college students involves giving the name of an actor and then trying to connect that actor with actor Kevin Bacon, counting the number of steps needed. For example, Sarah Jessica Parker has a “Bacon number” of 1 because she appeared in the same movie as Kevin Bacon, Footloose (1984). Will Smith has a Bacon number of 2. He has never appeared in a movie with Kevin Bacon; however, he was in Bad Boys II (2003) with Michael Shannon, who was in The Woodsman (2004)
with Kevin Bacon. Display 2.95 gives the number of links required to connect each of the 645,957 actors in the Internet Movie Database to Kevin Bacon.
Display 2.95 Bacon numbers.[Source: www.cs.virginia .edu.]
a. How many people have appeared in a movie with Kevin Bacon?
b. Who is the person with Bacon number 0? It has been questioned whether Kevin Bacon was the best choice for the “center of the Hollywood universe.” A possible challenger is Sean Connery. See Display 2.96.
Display 2.96 Connery numbers.
c. Do you think Kevin Bacon or Sean Connery better deserves the title “Hollywood center”? Make your case using statistical evidence (as always). d. (For movie fans.) What is Bacon’s
Connery number? What is Connery’s Bacon number?
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