3. Workplace Drug Testing Find the mean and standard deviation for the numbers of workers in groups of ten who test positive for illegal drugs. 4.Workplace Drug Testing If none of the ten workers tests positive for illegal drugs, is that a significantly low result? 5.Workplace Drug Testing If four of the ten workers test positive for illegal drugs, is that a significantly high result? 6. AcrophobiaUSA Today reported results from a survey in which subjects were asked if they are afraid of heights in tall buildings. The results are summarized in the accompanying table. Does this table describe a probability distribution? Why or why not? Response P(x) Yes 0.46 No 0.54 7.Brand Recognition In a study of brand recognition of Sony, groups of four consumers are interviewed. If x is the number of people in the group who recognize the Sony brand name, then x can be 0, 1, 2, 3, or 4, and the corresponding probabilities are 0.0016, 0.0250, 0.1432, 0.3892, and 0.4096. Does the given information describe a probability distribution? Why or why not? 8. Family>Partner Groups of people aged 15–65 are randomly selected and arranged in groups of six. The random variable x is the number in the group who say that their family and>or partner contribute most to their happiness (based on a Coca-Cola survey). The accompanying table lists the values of x along with their corresponding probabilities. Does the table describe a probability distribution? If so, find the mean and standard deviation. x P(x) 0 0+ 1 0.003 2 0.025 3 0.111 4 0.279 5 0.373 6 0.208 9.Detecting Fraud The Brooklyn District Attorney’s office analyzed the leading (leftmost) digits of check amounts in order to identify fraud. The leading digit of 1 is expected to occur 30.1% of the time, according to “Benford’s law,” which applies in this case. Among 784 checks issued by a suspect company, there were none with amounts that had a leading digit of 1. a. If there is a 30.1% chance that the leading digit of the check amount is 1, what is the expected number of checks among 784 that should have a leading digit of 1? b. Assume that groups of 784 checks are randomly selected. Find the mean and standard deviation for the numbers of checks with amounts having a leading digit of 1. c. Use the results from part (b) and the range rule of thumb to identify the values that are significantly low. d. Given that the 784 actual check amounts had no leading digits of 1, is there very strong evidence that the suspect checks are very different from the expected results? Why or why not? 10. Poisson: Deaths Currently, an average of 7 residents of the village of Westport (population 760) die each year (based on data from the U.S. National Center for Health Statistics). a. Find the mean number of deaths per day. b. Find the probability that on a given day, there are no deaths. c. Find the probability that on a given day, there is more than one death. d. Based on the preceding results, should Westport have a contingency plan to handle more than one death per day? Why or why not? 1. Planets The planets of the solar system have the numbers of moons listed below in order from the sun. (Pluto is not included because it was uninvited from the solar system party in 2006.) Include appropriate units whenever relevant. 00121728218 a. Find the mean. b. Find the median. Cumulative Review Exercises continued CHAPTER 5 Cumulative Review Exercises 239
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