Question

A philosophy professor assigned letter grades on its test according to the following schemeScores on the test are normally distributed with a mean of 81.2 and a standard deviation of 8.1Find the minimum score required for an A grade round your answer to the nearest whole number if necessary

Answer 1

Solution:

Given;

$\mu=81.2,\sigma=8.1,P(A)=0.12$

The z-score of the probability is 1.175.

Thus, using the z-score formula;

$\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \\ 1.175=\frac{x-81.2}{8.1} \\ \\ x\approx91 \end{gathered}$

The minimum score