Teenagers' Music and Lifestyle. Every year, USA Weekend conducts a survey of the nation's teenagers, asking them various questions about lifestyle and music. Nearly 60,000 teenagers responded to the survey, conducted in part through a Web site. Use this information for Exercises 82 and 83.

Question 5.83

teenmusic

83. Another survey question asked by USA Weekend was “If you had to choose just one type of music to listen to exclusively, which would it be?” The results are shown in the table.

Hip-hop/rap 27%
Pop 23%
Rock/punk 17%
Alternative 7%
Christian/gospel 6%
R&B 6%
Country 5%
Techno/house 4%
Jazz 1%
Other 4%

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  1. Construct a probability model.
  2. Is it unusual for a respondent to prefer jazz?
  3. Use technology to draw random samples of sizes 10, 100, 1,000, and 10,000 from your probability model.
  4. What can you conclude about the relative frequencies as the sample size increases?

5.1.83

(a)

Type of music Probability
Hip-hop/rap 0.27
Pop 0.23
Rock/Punk 0.17
Alternative 0.07
Christian/gospel 0.06
R&B 0.06
Country 0.05
Techno/house 0.04
Jazz 0.01
Other 0.04

(b) Yes. (c) Answers will vary. (d) As the sample size increases, the relative frequencies approach the probabilities.