Question

A division-wide aptitude test in Science was conducted to 1000 pupils. The mean of the test is 58 and the standard deviation is 12. The scores also approximate the normal distribution. What is the score that divides the distribution into two such that 75% of the cases is below it?

Answer 1

Population mean $\mu=58$

Standard deviation $\sigma=12$

Probability for the $75$^th percentile

$=0.75$

$Z ~for~P~of~0.75$

$=0.674$

$Z=\dfrac{X-\mu}{\sigma}~~~~~~X=σZ+\mu$

$X=12(0.674)+58$

$~~~~~=66.088$

$~~~~~\approx 66.0$