818 CHAPTER 12 Statistics Exercises Warm Up Exercises In Exercises 1–10, fill in the blank with an appropriate word, phrase, or symbol(s). 1. A distribution in which all the data values have about the same frequency is called a(n) _______ distribution. Rectangular 2. A distribution in which the frequency is either constantly increasing or constantly decreasing is called a(n) _______ distribution. J-shaped 3. a) A distribution that has a “tail” on its right is skewed to the _______. Right b) A distribution that has a “tail” on its left is skewed to the _______. Left 4. A distribution in which two nonadjacent data values occur more frequently than any other values in a set of data is called a(n) _______ distribution. Bimodal 5. A normal distribution is a(n) _______ shaped distribution. Bell 6. A measure of how far, in terms of standard deviations, a given data value is from the mean is called a z-score or a(n) _______ score. Standard 7. The mean of a set of data will always have a z-score of _______. 0 8. a) A data value that has a negative z-score is _______ the mean. Below b) A data value that has a positive z-score is _______ the mean. Above 9. According to the empirical rule, in a normal distribution, a) approximately _______ of the data lie within plus or minus1 standard deviation of the mean. 68% b) approximately _______ of the data lie within plus or minus 2 standard deviations of the mean, and 95% c) approximately _______ of the data lie within plus or minus 3 standard deviations of the mean. 99.7% 10. In a normal distribution, the mean, median, and mode all have the same _______. Value Practice the Skills In Exercises 11–14, give an example of the type of distribution. 11. Rectangular Answers will vary. 12. Skewed Answers will vary. 13. J-shaped Answers will vary. 14. Bimodal Answers will vary. 15. A normal distribution has a mean of 20 and a standard deviation of 2. Determine z-scores for the following data values. a) 22 1 b) 18 −1 c) 23 1.5 d) 15 −2.5 16. A normal distribution has a mean of 45 and a standard deviation of 5. Determine z-scores for the following data values. a) 48 0.6 b) 57 2.4 c) 37 −1.6 d) 45 0 For the distributions in Exercises 17–24, state whether you think the distribution would be normal, J-shaped, bimodal, rectangular, skewed left, or skewed right. 17. The wingspan of a full-grown red-tailed hawk Normal 18. The numbers resulting from tossing a die many times Rectangular 19. The number of people per household in the United States Skewed right 20. The heights of a sample of high school seniors, where there are an equal number of males and females Bimodal 21. Peak hours at a restaurant that only serves lunch and dinner Bimodal 22. The wearout mileage of automobile tires Normal 23. A spinner can land on equally sized sectors of a circle labeled 1– 4, respectively. The number resulting from spinning the spinner many times Rectangular 24. The number of children per family Skewed right In Exercises 25–36, use Table 12.8 to determine the specified area. 25. Above the mean 0.5000 26. Below the mean 0.5000 27. Between one standard deviation below the mean and two standard deviations above the mean 0.8185 28. Between 1.30 and 1.70 standard deviations above the mean 0.0522 29. To the left of = z 2.43 0.9925 30. To the left of = z 1.87 0.9693 Phoo Chan/Shutterstock SECTION 12.5
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