Answer to Question #325380 in Statistics and Probability for Zsa

Question

The result of NAT scores in Mathematics are normally distributed with μ=70 and σ=10. What is the percentile rank of a score of 75?

Answer 1

We have a normal distribution, $\mu=70, \sigma=10,x=75.$

Let's convert it to the standard normal distribution,

$z=\cfrac{x-\mu}{\sigma}=\cfrac{75-70}{10}=0.50;\\ P(X<75)=P(Z<0.50)=\\ =0.6915=69.15\% \text{ (from z-table).}$