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LIL The distribution of the annual incomes of a group of middle-management employees at deviation of $800. Compton Plastics approximates a normal distribution with a mean of $47,200 and a standard LF - REVIEW (a) About 68% of the incomes lie between what two amounts? (b) 7-3 About 95% of the incomes lie between what two amounts? (C) Virtually all of the incomes lie between what two amounts? (d) What are the median and the modal incomes? (e) Is the distribution of incomes symmetrical? RCISES 7. Explain what is meant by this statement: "There is not just one normal probability distribu- tion but a 'family' of them." 8. List the major characteristics of a normal probability distribution. 9. The mean of a normal probability distribution is 500; the standard deviation is 10. a. About 68% of the observations lie between what two values? b. About 95% of the observations lie between what two values? sewzed piss| nileub c. Practically all of the observations lie between what two values? goibmt bas 10. The mean of a normal probability distribution is 60; the standard deviation is 5. a. About what percent of the observations lie between 55 and 65? in be b. About what percent of the observations lie between 50 and 70? c. About what percent of the observations lie between 45 and 75? 11. The Kamp family has twins, Rob and Rachel. Both Rob and Rachel graduated from college 2 years ago, and each is now saming $50,000 per year. Rachel works in the retail industry, where the mean salary for executives with less than 5 years' experience is $35,000 with a standard deviation of $8,000. Hob is an engineer. The mean salary for engineers with less than 5 years' experience is $60,000 with a standard deviation of $5,000. Compute the z values for both Rob and Rachel and comment on your findings. 12. A recent article in the Cincinnati Enquirer reported that the mean labor cost to repair a heat pump is $90 with a standard deviation of $22. Monte's Plumbing and Heating Service com- pleted repairs on two heat pumps this morning. The labor cost for the first was $75 and it was $100 for the second. Assume the distribution of labor costs follows the normal prob- ability distribution. Compute z values for each and comment on your findings.The temperature of coffee sold at the Coffee Bean Cafe follows the normal probability distribu- tion, with a mean of 150 degrees. The standard deviation of this distribution is 5 degrees. n - 2 (a) What is the probability that the coffee temperature is between 150 degrees and 154 degrees? SELF - REVIEW (b) What is the probability that the coffee temperature is more than 164 degrees? 7-4 XERCISES 13. A normal population has a mean of 20.0 and a standard deviation of 4.0. a. Compute the z value associated with 25.0. b. What proportion of the population is between 20.0 and 25.0? c. What proportion of the population is less than 18.0? 14. A normal population has a mean of 12.2 and a standard deviation of 2.5. a. Compute the z value associated with 14.3. b. What proportion of the population is between 12.2 and 14.3? c. What proportion of the population is less than 10.0? 15. A recent study of the hourly wages of maintenance crew members for major airli showed that the mean hourly salary was $20.50, with a standard deviation of $3 Assume the distribution of hourly wages follows the normal probability distribution. select a crew member at random, what is the probability the crew member earns: a. Between $20.50 and $24.00 per hour? b. More than $24.00 per hour? c. Less than $19 00 per hour? 16. The mean of a normal probability distribution is 400 pounds. The standard deviat 10 pounds. a. What is the area between 415 pounds and the mean of 400 pounds? b. What is the area between the mean and 395 pounds? c. What is the probability of selecting a value at random and discovering that it has of less than 395 pounds