Question

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.

Answer 1

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.