Question

Scores from an exam are normally distributed with a mean of 85 and a standard deviation of 5. Suppose 188 students take the exam. About how many would receive a score above 80?
158 students

60 students

122 students

153 students

Answer 1

The mean is $\mu=85$ and standard deviation is $\sigma=5$. Then the variable $X\sim N(85,5)$.

Use substitution $Z=\dfrac{X-\mu}{\sigma}=\dfrac{X-85}{5}$, then the variable $Z\sim N(0,1)$.

The probability $Pr(X>80)$ can be calculated in the following way:

for X=80, $Z=\dfrac{80-85}{5} =-1$ and $Pr(X>80)=Pr(Z>-1)$. From the diagram $Pr(Z>-1)=0.34+0.34+0.135+0.025=0.84$.

Conclusion: if 188 students take the exam, then 188·0.84=157.92 (157) would receive a score above 80

Answer 2

158 students is correct on grad point