268 CHAPTER 6 Normal Probability Distributions Statistical Literacy and Critical Thinking 1. Hershey Kisses Based on Data Set 38 “Candies” in Appendix B, weights of the chocolate in Hershey Kisses are normally distributed with a mean of 4.5338 g and a standard deviation of 0.1039 g. a. What are the values of the mean and standard deviation after converting all weights of Hershey Kisses to z scores using z = 1x - m2>s? b. The original weights are in grams. What are the units of the corresponding z scores? 2. Hershey Kisses Based on Data Set 38 “Candies” in Appendix B, weights of the chocolate in Hershey Kisses are normally distributed with a mean of 4.5338 g and a standard deviation of 0.1039 g. a. For the bell-shaped graph of the normal distribution of weights of Hershey Kisses, what is the area under the curve? b. What is the value of the median? c. What is the value of the mode? d. What is the value of the variance? 3. Normal Distributions Is the distribution described in the preceding exercise a standard normal distribution? Why or why not? 4. Mega Millions The Mega Millions lottery game requires that a number between 1 and 25 is randomly selected. What is the shape of the distribution of those selected numbers? Is it correct to say that because these selected numbers are the result of the normal selection procedure used for every drawing, the distribution of the selected numbers is a normal distribution? IQ Scores. In Exercises 5–8, find the area of the shaded region. The graphs depict IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler IQ test). 5. 118 6. 91 7. 79 133 8. 112 124 6-2 Basic Skills and Concepts
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