The scores of 12thgrade students on the National Assessment

The scores of 12th-grade students on the National Assessment of Educational Progress year 2000 mathematics test have a distribution that is approximately Normal with mean ? = 300 and standard deviation ? = 33. Choose one 12th-grader at random. What is the probability (0.1) that his or her score is higher than 300? Higher than 399 (0.001)? Now choose an SRS of 4 twelfth-graders and calculate their mean score . If you did this many times, what would be the mean of all the -values? What would be the standard deviation (0.1) of all the -values? What is the probability that the mean score for your SRS is higher than 300? (0.1) Higher than 399? (0.0001)

Solution

What is the probability (0.1) that his or her score is higher than 300?

P(X>300) = P((X-mean)/s >(300-300)/33)

=P(Z>0)=0.5 (from standard normal table)

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Higher than 399 (0.001)?

P(X>399) = P(Z>(399-300)/33)

=P(Z>3) =0.0013 (from standard normal table)

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Now choose an SRS of 4 twelfth-graders and calculate their mean score . If you did this many times, what would be the mean of all the -values?

mean=300

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What would be the standard deviation (0.1) of all the -values?

standard deviatoin =s/vn

=33/sqrt(4)

=16.5

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What is the probability that the mean score for your SRS is higher than 300? (0.1)

P(xbar>300) = P(Z>(300-300)/16.5)

=P(Z>0)=0.5 (from standard normal table)

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Higher than 399? (0.0001)

P(xbar>300) = P(Z>(399-300)/16.5)

=P(Z>6)=0 (from standard normal table)