Question

The scores on an exam are normally distributed with a mean of 77 and a standard deviation of 10. What percent of the scores are greater than 87?

68%
16%
84%
2.5%

Answer 1

Answer: 16%

Explanation:

Given: The scores on an exam are normally distributed.

Mean :
`\mu=77`

Standard deviation=
`\sigma=10`

Let X = 87

Then,
`z=(X-\mu)/(\sigma)`

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

Now, the probability of scores are greater than 87 is given by :-

`P(X\geq87)=1-P(X\leq87)`

Since,
`P(X\leq 87)=\text{p value of z=1}=0.8413447`

Then,
`P(X\geq87)=1-0.8413447=0.1586553`

In percent ,
`P(X\geq87)=0.1586553*100=15.86\approx16%`

Answer 2

The correct answer between all the choices given is the second choice, which is 16%. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.