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V125BC [204]
3 years ago
12

A standard chemistry examination administered nationally by the American Chemical Society has a mean of 500 and a standard devia

tion of 90. What is the probability that the average of a random sample of examination scores of 25 students will be between 450 and 500?
Mathematics
1 answer:
Maslowich3 years ago
4 0
Let X be a random sample representing the score of a student in the American Chemical Society Examination.
P(450 < x < 500) = P((450 - 500)/(90/sqrt(25)) < z < (500 - 500)/(90/sqrt(25))) = P(-2.778 < z < 0) = P(z < 0) - P(z < -2.778) = P(z < 0) - [1 - P(z < 2.778)] = P(z < 0) + P(z < 2.778) - 1 = 0.5 + 0.99727 - 1 = 0.49727 = 49.7%
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