CHAPTER 6 Review Exercises 305 4. Arm Circumferences Arm circumferences of adult men are normally distributed with a mean of 33.64 cm and a standard deviation of 4.14 cm (based on Data Set 1 “Body Data” in Appendix B). A sample of 25 men is randomly selected and the mean of the arm circumferences is obtained. a. Describe the distribution of such sample means. b. What is the mean of all such sample means? c. What is the standard deviation of all such sample means? 5. Birth Weights Based on Data Set 6 “Births” in Appendix B, birth weights of girls are normally distributed with a mean of 3037.1 g and a standard deviation of 706.3 g. a. For the bell-shaped graph, 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? 6. Mensa Membership in Mensa requires a score in the top 2% on a standard intelligence test. The Wechsler IQ test is designed for a mean of 100 and a standard deviation of 15, and scores are normally distributed. a. Find the minimum Wechsler IQ test score that satisfies the Mensa requirement. b. If 4 randomly selected adults take the Wechsler IQ test, find the probability that their mean score is at least 131. c. If 4 subjects take the Wechsler IQ test and they have a mean of 131 but the individual scores are lost, can we conclude that all 4 of them have scores of at least 131? 7. Tall Clubs The social organization Tall Clubs International has a requirement that women must be at least 70 in. tall. Assume that women have normally distributed heights with a mean of 63.7 in. and a standard deviation of 2.9 in. (based on Data Set 1 “Body Data” in Appendix B). a. Find the percentage of women who satisfy the height requirement. b. If the height requirement is to be changed so that the tallest 2.5% of women are eligible, what is the new height requirement? In Exercises 8 and 9, assume that women have standing eye heights that are normally distributed with a mean of 59.7 in. and a standard deviation of 2.5 in. (based on anthropometric survey data from Gordon, Churchill, et al.). 8. Biometric Security In designing a security system based on eye (iris) recognition, we must consider the standing eye heights of women. a. If an eye recognition security system is positioned at a height that is uncomfortable for women with standing eye heights less than 54 in., what percentage of women will find that height uncomfortable? b. In positioning the eye recognition security system, we want it to be suitable for the lowest 95% of standing eye heights of women. What standing eye height of women separates the lowest 95% of standing eye heights from the highest 5%? 9. Significance Instead of using 0.05 for identifying significant values, use the criteria that a value x is significantly high if P1x or greater2 … 0.01 and a value is significantly low if P1x or less2 … 0.01. Find the standing eye heights of women that separate significant values from those that are not significant. Using these criteria, is a woman’s standing eye height of 67 in. significantly high? 10. Assessing Normality Listed below are the recent salaries (in millions of dollars) of players on the LA Lakers professional basketball team. Do these salaries appear to come from a population that has a normal distribution? Why or why not? 35.6 14.4 12.0 9.0 7.5 5.8 4.4 3.5 2.4 1.8 1.7 1.7 1.5 1.5 1.0 0.1 0.1
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