Question

The scores on an exam are normally distributed, with a mean of 77 and a standard deviation of 10. What percentage of the scores are greater than 87? 34% 50% 84% 16%

Answer 1

Given

`\begin{gathered} \mu=77 \\ \sigma=10 \end{gathered}`

The z-score formula is

`z=(x-\mu)/(\sigma)`

In our case,

`\Rightarrow z=(87-77)/(10)=(10)/(10)=1`

Using a z-score table,

`\Rightarrow P(X<87)=0.8413`

Then,

`\begin{gathered} P(X>87)=1-P(X<87)=1-0.8413=0.1587=15.87\% \\ \Rightarrow P(X>87)\approx16\% \end{gathered}`

Thus, the answer is 16%