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 73 and a standard deviation of 15. Answer each of the following questions by using the Empirical rule, (please enter numbers with a percent sign). What percent of the students who take the exam score between 73 and 88? Any student who scores higher than 103 is automatically admitted to the college. What percent of the students who take the exam are automatically admitted to the college? What percent of the students who take the exam score between 58 and 103? What percent of the students who take the exam score less than 43 or higher than 103?

Explanation / Answer

a)

Note that 73 is the mean, and 88 is 1 standard deviation above the mean. By 68-95-99.7 rule and symmetry considerations,

P(73<x<88) = 68/2 % = 34% [ANSWER]

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b)

Note that 103 is 2 standard deviations above the mean. By 68-95-99.7 rule and symmetry considerations,

P(x>103) = (100 - 95)/2 = 2.5% [ANSWER]

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c)

Note that 58 is 1 standard deviation below the mean.

Note that 103 is 2 standard deviations above the mean.

By 68-95-99.7 rule and symmetry considerations,

P(58<x<103) = (68 + 95)/2 % = 81.5% [ANSWER]

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d)

Note that 43 and 103 are both 2 standard deviations from the mean.

By 68-95-99.7 rule and symmetry considerations,

P(outide 43<x<103) = 100 - 95 % = 5% [ANSWER]

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