Question

The results of a nationwide aptitude test in mathematics are normally distributed with the mean=63 and standard deviation=5. What is the 97.5th percentile?

Answer 1

The following are the population mean (μ), population standard deviation (σ) and cumulative probability provided:

Population Mean (μ) =63

Population Standard Deviation (σ) =5

Cumulative Probability =0.975

First, we corresponding z score so that the cumulative standard normal probability distribution is equal to 0.975

By using a normal distribution table , we find that $z_c = 1.96$

Hence, the X score associated with a cumulative probability of 0.975

$X ​ = ​ μ+z c ​ ×σ$

$=63+1.96×5= 72.8 ​$