Suppose that the test scores for a particular college entrance exam are distribu

Question

Suppose that the test scores for a particular college entrance exam are distributed according to a bell-shaped, symmetric distribution with a mean of 450 and a standard deviation of 100. Answer each of the following questions by using the Empirical rule. (a) What percent of the students who take the exam score between 350 and 550? (b) Any student who scores higher than 550 is automatically admitted to the college. What percent of the students who take the exam are automatically admitted to the college? (c) What percent of the students who take the exam score between 250 and 350? (d) What percent of the students who take the exam score less than 250 or higher than 650

Explanation / Answer

(a) What percent of the students who take the exam score between 350 and 550?

Here, 350 and 550 are both 1 standard deviation away from the mean. By 68-95-99.7 rule,

P(350<x<550) = 68% [ANSWER]

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(b) Any student who scores higher than 550 is automatically admitted to the college. What percent of the students who take the exam are automatically admitted to the college?

Here, 550 is 1 standard deviation above the mean. By 68-95-99.7 rule and symmetry considerations,

P(x>550) = (100-68)/2 = 16% [ANSWER]

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(c) What percent of the students who take the exam score between 250 and 350?

Note that 250 is 2 standard deviations below the mean, and 350 is 1 standard deviation below the mean. By 68-95-99.7 rule and symmetry considerations,

P(250<x<350) = (95 - 68)/2 % = 13.5% [ANSWER]

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(d) What percent of the students who take the exam score less than 250 or higher than 650

Here, 250 and 650 are both 2 standard deviations away from the mean. By 68-95-99.7 rule and symmetry considerations,

P(outside 250<x<650) = 100 - 95 % = 5% [ANSWER]

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