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Given the z scores of reading is 0.5, math is -3 and science is 2.25 What proportion of the normal distribution corresponds to z-score values greater than the child’s z-score on the science test.

User Adam Taylor
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1 Answer

18 votes
18 votes

Given that the z-score of science is 2.25, the proportion of values greater than this is calculated as,


P(z>2.25)=P(z>0)-P(0Since the normal curve is symmetric, the area after z=0 is 0.5,[tex]P(z>2.25)=0.5-\emptyset(2.25)

From the Standard Normal Distribution Table,


\emptyset(2.25)=0.4878

Substitute this value,


\begin{gathered} P(z>2.25)=0.5-0.4878 \\ P(z>2.25)=0.0122 \end{gathered}

Thus, 0.0122 proportion of the normal distribution corresponds to z-score values greater than the child’s z-score on the science test.

User ValentiGoClimb
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