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Raw scores on behavioral tests are often transformed for easier comparison. A test of reading ability...

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Statistics

Raw scores on behavioral tests are often transformed for easiercomparison. A test of reading ability has mean 55 and standarddeviation 5 when given to third graders. Sixth graders have meanscore 77 and standard deviation 7 on the same test. To provideseparate \"norms\" for each grade, we want scores in each grade tohave mean 100 and standard deviation 20. (Round your answers to twodecimal places.)

(a) What linear transformation will change third-grade scores xinto new scores xnew = a + bx that have the desired mean andstandard deviation? (Use b > 0 to preserve the order of thescores.)

a =

b =


(b) Do the same for the sixth-grade scores.

a =

b =


(c) David is a third-grade student who scores 75 on the test. FindDavid's transformed score.


Nancy is a sixth-grade student who scores 75. What is hertransformed score?


Who scores higher within his or her grade?

Answer & Explanation Solved by verified expert
4.2 Ratings (819 Votes)
aThird grade scoresMean 55SD sx 5y a bxmean of y a b X mean of x100 a 55b1Variance of y b2 X    See Answer
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