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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%

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The correct
answer between all the choices given is the second choice, which is 16%. I am
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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 , \(P(X\geq87)=0.1586553\times100=15.86\approx16%\)

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