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On an exam, the mean score is 78 points, with a standard deviation of 6 points. Assuming normal distribution of the scores, approximately what percentage of students received more than 85?A.12% B.17% C.8% D.9% E.None of the above

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JeanaShupp

Answer: A. 12%

Step-by-step explanation:-

Given : In an exam , Mean score : [tex]\mu=78\text{ points}[/tex]

Standard deviation : [tex]6\text{ points}[/tex]

Let X be a random variable that represents the scores of students.

We assume that the points are normally distributed.

Z-score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x = 85, we have

[tex]z=\dfrac{85-78}{6}\approx1.17[/tex]

Then using standard normal distribution table, the probability that the students received more than 85 is given by :-

[tex]P(x>85)=P(z>1.17)=1-P(z<1.17)\\\\=1-0.8789995=0.1210005\approx0.12=12\%[/tex]

Hence, the percentage of students received more than 85 =12%

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