Question

The gpa at the super university has a normal distribution with a mean 2.29 and standard deviation 1.29 to be an honors student at this university your GPA has to be in the top 20% what is the smallest gpa you need to have to be an honors student?

Answer 1

The smallest GPA needed to fall in the top 20% is
`g`, where


`\mathbb P(G\ge g)=0.20`

where
`G` is a random variable denoting GPA scores. Transform
`G` to the standard normal random variable
`Z` using


`Z=(G-\mu_G)/(\sigma_G)\iff G=\mu_G+\sigma_GZ`

where
`\mu_G` and
`\sigma_G` are the mean and standard deviation of
`G`, respectively. Now


`\mathbb P(G\ge g)=\mathbb P\left(Z\ge(g-2.29)/(1.29)\right)=0.20`

Using the inverse CDF for the standard normal distribution, we find that the corresponding critical value is about 0.8416, which means


`\implies(g-2.29)/(1.29)\approx0.8416\implies g\approx3.3757`