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

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.

Answer 2

Answer:  16%

Step-by-step explanation:

Given: The scores on an exam are normally distributed.

Mean : $\mu=77$

Standard deviation=$\sigma=10$

Let X = 87

Then, $z=\dfrac{X-\mu}{\sigma}$

$\Rightarrow\ z=\dfrac{87-77}{10}=1$

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 , $P(X\geq87)=0.1586553\times100=15.86\approx16%$