Question

You are looking at taking two professors for a course. The first professor has an average grade of 85% with a standard deviation of 2%. The second professor has an average grade of 50% with a standard deviation of 15%. What is the probability you pass the second professor'sclass?A) 0.91B) 0.09

Answer 1

Given the formula

`\sigma^2=\mu(1-p)`
`\begin{gathered} \text{where }\sigma=\text{standard deviation} \\ \mu=the\text{ average grade} \\ p=\text{ probability of passing the course} \end{gathered}`
`\begin{gathered} \mu=50\text{ \%=}(50)/(100)=0.5 \\ \sigma=\text{ 15\%=}\frac{\text{15}}{100}=0.15 \end{gathered}`
`\begin{gathered} 0.15^2=0.5(1-p) \\ 0.0225=0.5(1-p) \\ \text{Divide both sides by 0.5} \\ (0.0225)/(0.5)=1-p \\ 0.045=1-p \\ \text{collect like terms} \\ p=1-0.045 \\ p=0.955 \end{gathered}`

Hence, the probability that the student passes the second professor's class is 0.955.