Question

The scores on the verbal section of a Graduate RecordExam are Normally distributed with a mean of 470 and astandard deviation of 120. Sheila scored 610 on thisportion of her exam.

Answer 1

`\begin{gathered} \text{Given} \\ \mu=470 \\ \sigma=120 \\ x=610 \end{gathered}`

Find the z-score of Sheila's score.

`\begin{gathered} z=(x-\mu)/(\sigma) \\ z=(610-470)/(120) \\ z=(140)/(120) \\ z=1.17 \end{gathered}`

Since we are looking for the percent of takers that earned a higher score then Sheila, find P( z > 1.17)

Looking at the value to the left of the z-score we have

`\begin{gathered} P(z>1.17)=1-0.87900 \\ P(z>1.17)=0.121 \end{gathered}`

Multiply by 100% and we get

`0.121\cdot100\%=12.1\%`

Rounding to the nearest whole number, the percent of takers who earned a higher score than Sheila is 12%