Answer to Question #335088 in Statistics and Probability for sofia

Question

the result of a nationwide aptitude test in mathematics are normally distributed with μ 80 and σ 15. what is the score that divides the distribution such that 99% of the cases is below it

Answer 1

$\mu=80, \sigma=15.$

The 99th percentile of a normal distribution is $z=2.326\text{ (find from z-table)};$

$P(Z<2.326)=0.99;\\ z=\cfrac{x-\mu}{\sigma};\\$

$x=z\sigma+\mu=2.326\cdot15+80=114.89.$

114.89 is the score that divides the distribution such that 99% of the cases is below it.