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

158 students is correct on grad point

Answer 2

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

Use substitution
`Z=(X-\mu)/(\sigma)=(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=(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