Question

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

Answer 1

Answer: A. 12%

Step-by-step explanation:-

Given : In an exam , Mean score : $\mu=78\text{ points}$

Standard deviation : $6\text{ points}$

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

We assume that the points are normally distributed.

Z-score : $z=\dfrac{x-\mu}{\sigma}$

For x = 85, we have

$z=\dfrac{85-78}{6}\approx1.17$

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

$P(x>85)=P(z>1.17)=1-P(z$

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