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zscorespractice_solutions

# zscorespractice_solutions - POLS 4150 Practice problems for...

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POLS 4150 – Practice problems for calculating areas under the normal curve In a large class, the average final exam score was 75 with a standard deviation of 8. Assume that the scores are distributed normally. Let X = exam score 1) What proportion of students scored above a 65? Z = (65-75) / 8 = -1.25 Area below -1.25 = 10.56% 100% - 10.56% = 89.44% 2) What proportion of students scored between an 81 and an 89? Z = (81-75) / 8 = .75. Area above .75 = 22.66% Z = (89-75) / 8 = 1.75. Area above 1.75 = 4.01% 22.66% - 4.01% = 18.65% 3) What proportion of students scored below a 61? Z = (61-75) / 8 = -1.75 Area below -1.75 = 4.01% 4) What proportion of students scored between a 61 and an 85? Z = (61-75) / 8 = -1. 75. Area below -1.75 = 4.01% Z = (85-75) / 8 = 1.25. Area above 1.25 = 10.56% 100% - (46.99% + 39.44%) = 85.43 5) What proportion of students scored above a 91? Z = (91-75) / 8 = 2.0 Area beyond Z = 2.28% 6) What proportion of students scored between 55 and 65? Z = (55-75) / 8 = -2.5. Area below -2.5 = 0.62% Z = (65-75) / 8 = -1.25. Area below -1.25 = 10.56% 10.56% - 0.62% = 9.94% 7) What proportion of students scored below an 89? Z = (89-75) / 8 = 1.75 Area above 1.75 = 4.01% 100% - 4.01% = 95.99%

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