Question

3. According to data, the mean quantitative score on a standardized test for female college-bound high school seniors was 500. The scores are approximately normally distributed with a population standard deviation of 100. What percentage of the female college-bound high school seniors had scores above 725? Use a standard normal table or appropriate technology.

Answer 1

Let X denotes the score on a standardized test for female college - bound high school seniors.

X ~ N ( 500 , 100 )

We have to compute P ( X > 725 )

$\dpi{100} \fn_jvn P ( X > 725) =P \left (\frac{X - \mu }{\sigma } > \frac{725-\mu }{\sigma } \right )$

  $\dpi{100} \fn_jvn =P \left ( Z> \frac{725-500 }{100} \right )$

  $\dpi{100} \fn_jvn =P \left ( Z> 2.25\right )$

$\dpi{100} \fn_jvn =0.0122$ { using standard normal table )