5.1 EXERCISES 242 CHAPTER 5 Normal Probability Distributions For Extra Help: MyLab Statistics Building Basic Skills and Vocabulary 1. Given the mean of a normal distribution, how can you find the median? 2. What is the total area under the normal curve? 3. Describe the inflection points on the graph of a normal distribution. At what x@values are the inflection points located? 4. Give two real-life examples of a continuous variable. Include one that is likely to be normally distributed. Explain your reasoning. 5. Draw two normal curves that have the same mean but different standard deviations. Describe the similarities and differences. 6. Draw two normal curves that have different means but the same standard deviation. Describe the similarities and differences. 7. What is the mean of the standard normal distribution? What is the standard deviation of the standard normal distribution? 8. Explain how to transform a given x@value of a normally distributed variable x into a z@score. 9. Getting at the Concept Why is it correct to say “a” normal distribution and “the” standard normal distribution? 10. Getting at the Concept A z@score is 0. Which of these statements must be true? Explain your reasoning. (a) The mean is 0. (b) The corresponding x@value is 0. (c) The corresponding x@value is equal to the mean. Graphical Analysis In Exercises 11–16, determine whether the graph could represent a variable with a normal distribution. Explain your reasoning. If the graph appears to represent a normal distribution, estimate the mean and standard deviation. 11. x 45 46 47 48 49 50 51 52 12. x 15 16 17 18 19 20 21 22 13. x 10 11 12 13 14 15 16 17 14. x 1 2 3 4 5 6 15. x 8 9 101112131415 16. x 12 13 14 15 16 17 18 19
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