SECTION 5.3 Normal Distributions: Finding Values 259 36. GRE Scores The test scores for the analytical writing section of the Graduate Record Examination (GRE) can be approximated by a normal distribution, as shown in the figure. (Source: Educational Testing Service) (a) What is the maximum score that can be in the bottom 20% of scores? (b) Between what two values does the middle 80% of the scores lie? 37. Red Blood Cell Count The red blood cell counts (in millions of cells per microliter) for a population of adult males can be approximated by a normal distribution, with a mean of 5.4 million cells per microliter and a standard deviation of 0.4 million cells per microliter. (a) What is the minimum red blood cell count that can be in the top 25% of counts? (b) What red blood cell counts would be considered unusual? 38. Pregnancy Length The pregnancy durations (in days) for a population of new mothers can be approximated by a normal distribution, with a mean of 267 days and a standard deviation of 10 days. (a) What is the minimum pregnancy durations that can be in the top 10% of pregnancy durations? (b) What pregnancy durations would be considered unusual? 39. Bags of Baby Carrots The weights of bags of baby carrots are normally distributed, with a mean of 32 ounces and a standard deviation of 0.36 ounce. Bags in the upper 4.5% are too heavy and must be repackaged. What is the most a bag of baby carrots can weigh and not need to be repackaged? 40. Writing a Guarantee You sell a brand of automobile tire that has a life expectancy that is normally distributed, with a mean life of 30,000 miles and a standard deviation of 2500 miles. You want to give a guarantee for free replacement of tires that do not wear well. You are willing to replace approximately 10% of the tires. How should you word your guarantee? Extending Concepts 41. Vending Machine A vending machine dispenses coffee into an eight-ounce cup. The amounts of coffee dispensed into the cup are normally distributed, with a standard deviation of 0.03 ounce. You can allow the cup to overflow 1% of the time. What amount should you set as the mean amount of coffee to be dispensed? 42. History Grades In a history class, the grades for various assessments are all positive numbers and have different distributions. Determine whether the grades for each assessment could be normally distributed. Explain your reasoning. (a) a midterm exam with a mean of 67, standard deviation of 15, and 75th percentile score of 77 (b) a final with a mean of 72, standard deviation of 9, and 90th percentile score of 93 (c) a quiz with a mean of 33, a 40th percentile of 30, and a 60th percentile of 39 (d) a homework assignment with a mean of 19, a 10th percentile of 7, and a 90th percentile of 31 (e) an extra credit assignment with a mean of 2.25 and a standard deviation of 2.49 (f) a research paper with a 35th percentile of 120, a 65th percentile of 160, and an 80th percentile of 200 x = 3.58 μ = 0.85 σ GRE Analytical Writing Scores Score 1 2 3 4 5 6 FIGURE FOR EXERCISE 36
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