Question

Suppose ACT Reading scores are normally distributed with a mean of 21.3 and a standard deviation of 5.9. A university plans to award scholarships to students whose scores are in the top 7%. What is the minimum score required for the scholarship? Round your answer to the nearest tenth, if necessary.

Answer 1

Answer:

30.0

Step-by-step explanation:

Given our data is normally distribute with $\mu=21.3$ and $\sigma=5.9$

-Top 7% is given by find the z-value corresponding to p=(1-0.07)=0.93

-We substitute our values in the equation below;

$z=\frac{\bar X-\mu}{\sigma}\\\\\\=\frac{X-21.3}{5.9}, z_{0.035}=1.476\\\\\therefore 1.476=\frac{X-21.3}{5.9}\\\\X=5.9\times 1.476+21.3\\\\=30.0084\approx30.0$

Hence, the minimum score required for the scholarship is 30.0