The average score of 100 students taking a statistics final was 70 with a standard deviation of 7. Assuming a normal distribution, approximately how many scored greater than 65?
A) 0.2611
B) 0.2389
C) 0.7611
D) -0.714

Question

Quizplus · Accepted Answer

To find the number of students who scored greater than 65, we first calculate the z-score for a score of 65. The z-score formula is $z = \frac{(X - \mu)}{\sigma}$, where $X$ is the score, $\mu$ is the mean, and $\sigma$ is the standard deviation. Plugging in the values, we get $z = \frac{(65 - 70)}{7} = -0.714$. Looking up -0.714 on the standard normal distribution table, we find that approximately 0.2389 of the distribution lies below this z-score. Since we're interested in those who scored greater than 65, we subtract this from 1 (since the total area under the curve is 1) to get 1 - 0.2389 = 0.7611. This means approximately 76.11% of the students scored above 65. Since there are 100 students, approximately 76 students scored greater than 65.

The Average Score of 100 Students Taking a Statistics Final