Suppose anexam has 50 questions each worth 2 points. The results for thisexam fo

Question

Suppose anexam has 50 questions each worth 2 points. The results for thisexam follow a normal distribution where the mean is 80 points witha standard deviation of 6 points.

PartA:    Approximately 95% of the exam scores willbe between what two values?

a.     (80± 6) = (74 to 86) points

b.    (80 ± 2 ´ 6) = (80 ± 12) =(68 to 92) points

c.     (80 ± 3 ´ 6) = (80 ±18) = (62 to 98) points

d.    (80 ± 2) = (78 to 82) points

PartB: Would you expect a student to score as lowas 50 points on this exam? Provide reasoning.

Explanation / Answer

95% of the exam scores will fall within 2 standard deviationsof the mean (12 points either way), so the answer is b. You wouldn't expect a student to score as low as 50 pointsbecause in a normal distribution 99% will score within 3 standarddeviations of the mean. Therefore, 80-(6x3) = 62. It is highlyunlikely that someone would score 50.

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