250 CHAPTER 5 Normal Probability Distributions Graphical Analysis In Exercises 13–16, a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded region of the graph. Assume the variable x is normally distributed. 13. x Score = 1051 μ = 211 σ SAT Total Scores 750 < x < 1000 750 1000 1500 14. x Score = 20.7 μ = 5.9 σ ACT Composite Scores 25 < x < 30 6 25 30 (Source: College Board) (Source: ACT, Inc.) 15. x Pregnancy length (in days) = 267 μ = 10 σ Pregnancy Length in a Population of New Mothers 285 < x < 294 240 285 294 16. x Count (in million cells/microliter) = 5.4 μ = 0.4 σ Red Blood Cell Count in a Population of Adult Males 4.5 < x < 5.5 4.5 5.5 6.5 Using Normal Distributions In Exercises 17–20, answer the questions about the specified normal distribution. 17. SAT Total Scores Use the normal distribution in Exercise 13. (a) What percent of the SAT total scores are less than 1300? (b) Out of 1000 randomly selected SAT total scores, about how many would you expect to be greater than 1100? 18. ACT Composite Scores Use the normal distribution in Exercise 14. (a) What percent of the ACT composite scores are less than 19? (b) Out of 1500 randomly selected ACT composite scores, about how many would you expect to be greater than 21? 19. Pregnancy Length Use the normal distribution in Exercise 15. (a) What percent of the new mothers had a pregnancy length of less than 290 days? (b) What percent of the new mothers had a pregnancy length of between 260 and 300 days? (c) Out of 250 randomly selected new mothers, about how many would you expect to have had a pregnancy length of greater than 287 days? 20. Red Blood Cell Count Use the normal distribution in Exercise 16. (a) What percent of the adult males have a red blood cell count less than 6 million cells per microliter? (b) What percent of the adult males have a red blood cell count between 4.7 and 5.3 million cells per microliter? (c) Out of 200 randomly selected adult males, about how many would you expect to have a red blood cell count greater than 4.8 million cells per microliter?
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