Question

A college student takes a standardized test and scores a 163. if the mean is 155 and the standard deviation is 7, what is the student's percentile rank

Answer 1

`\mathbb P(X\le163)=\mathbb P\left(\frac{X-155}7\le\frac{163-155}7\right)\approx\mathbb P(Z\le1.1429)\approx0.8735`

which puts the student at about the 87th percentile.