The scores of 12th-grade students on the National Assessment of Educational Prog

Question

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)

Explanation / Answer

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)

--------------------------------------------------------------------------------------------------------------------

Higher than 399 (0.001)?

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

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

--------------------------------------------------------------------------------------------------------------------

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

--------------------------------------------------------------------------------------------------------------------

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

standard deviatoin =s/vn

=33/sqrt(4)

=16.5

--------------------------------------------------------------------------------------------------------------------

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)

--------------------------------------------------------------------------------------------------------------------

Higher than 399? (0.0001)

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

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

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.