Question

The scores on an economics examination are normally distributed with a mean of 73 and a standard deviation of 16. If the instructor assigns a grade of A to 12% of the class, what is the lowest score a student may have and still obtain an A?

Answer 1

So first we find the \(z\) score. \[
z=\frac{x-\mu}{\sigma} =\frac{x-73}{16}
\]

Answer 2

Now \(12\%\) gets and A, so we want to go from \(0\%\) to \(100\%-12\%=88\%\).
So look up \(z=\Phi ^{-1}(0.880)\) to get the standard score.
Then find the actual score by solving for \(x\)\[
\Phi ^{-1}(0.880)=\frac{x-73}{16}
\]

Answer 3

Now \(\Phi^{-1}(0.88)\approx 1.174987\) if you look it up.
So\[
x \approx 16(1.174987)+73\approx 91.799792
\]So you would want to get \(92\) points to be safe.