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Chapter 3: Problem 29
The mean age of six persons is 46 years. The ages of five of these six persons are \(57,39,44,51\), and 37 years, respectively. Find the age of the sixth person.
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The following data give the prices of seven textbooks randomly selected from a university bookstore. \(\begin{array}{lllllll}\$ 89 & \$ 170 & \$ 104 & \$ 113 & \$ 56 & \$ 161 & \$ 147\end{array}\) a. Find the mean for these data. Calculate the deviations of the data values from the mean. Is the sum of these deviations zero? b. Calculate the range, variance, and standard deviation.
In the Olympic Games, when events require a subjective judgment of an athlete's performance, the highest and lowest of the judges' scores may be dropped. Consider a gymnast whose performance is judged by seven judges and the highest and the lowest of the seven scores are dropped. a. Gymnast A's scores in this event are \(9.4,9.7,9.5,9.5,9.4,9.6\), and \(9.5 .\) Find this gymnast's mean score after dropping the highest and the lowest scores. b. The answer to part a is an example of (approximately) what percentage of trimmed mean? c. Write another set of scores for a gymnast B so that gymnast A has a higher mean score than gymnast B based on the trimmed mean, but gymnast B would win if all seven scores were counted. Do not use any scores lower than \(9.0\).
The following data are the ages (in years) of six students. \(\begin{array}{llllll}19 & 19 & 19 & 19 & 19 & 19\end{array}\) Calculate the standard deviation. Is its value zero? If yes, why?
Jeffrey is serving on a six-person jury for a personal-injury lawsuit. All six jurors want to award damages to the plaintiff but cannot agree on the amount of the award. The jurors have decided that each of them will suggest an amount that he or she thinks should be awarded; then they will use the mean of these six numbers as the award to recommend to the plaintiff. a. Jeffrey thinks the plaintiff should receive \(\$ 20,000\), but he thinks the mean of the other five jurors' recommendations will be about \(\$ 12,000\). He decides to suggest an inflated amount so that the mean for all six jurors is \(\$ 20,000\). What amount would Jeffrey have to suggest? b. How might this jury revise its procedure to prevent a juror like Jeffrey from having an undue influence on the amount of damages to be awarded to the plaintiff?
Assume that the annual earnings of all employees with CPA certification and 6 years of experience and working for large firms have a bell-shaped distribution with a mean of \(\$ 134,000\) and a standard deviation of \(\$ 12,000\). a. Using the empirical rule, find the percentage of all such employees whose annual earnings are hetween i. \(\$ 98,000\) and \(\$ 170,000\) ii. \(\$ 110,000\) and \(\$ 158,000\) "b. Using the empirical rule, find the interval that contains the annual earnings of \(68 \%\) of all such employees.
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