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^{-((x-\mu)/(2\sigma^2)}`

Then,

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

Now,

For second professor,

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

Now,

The probability that pass the second professor is,

`\begin{gathered} P=(0.099)/(0.1719) \\ =0.57 \end{gathered}`

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