Question

Which professor's class is easier to pass? Which professors class is it easier to get an A in?A) Easier to pass and get an A with the first professorB) Easier to pass the first professor and easier to get an A with the second professorC) Easier to pass and get an A with the second professorD) Easier to pass the second professor and get an A with the first professor

Answer 1

As per given by the question,

The average grade of the first professor is 85%, and their standard deviations is 2%.

The average grade of the second professor is 50%, and their standard deviations is 15%.

Now,

The standard deviation for first professor is denoted by

$\sigma=2$

The standard deviation of second professor is,

$\sigma=15$

Now,

from normal distribution formula,

$y=\frac{1}{\sigma\sqrt[]{2\pi}}e^{-\frac{(x-\mu}{2\sigma^2}}$

Then,

$\begin{gathered} y1=\frac{1}{2\sqrt[]{2\pi}}e^{-\frac{0.85}{8}} \\ =0.1719 \end{gathered}$

Now,

For second professor,

$\begin{gathered} y2=\frac{1}{15\sqrt[]{2\pi}}e^{-(\frac{0.50}{450}}) \\ =0.099 \end{gathered}$

Now,

The probability that pass the second professor is,

$\begin{gathered} P=\frac{0.099}{0.1719} \\ =0.57 \end{gathered}$

Hence, the probability that pass the second professor is 0.57.