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 less than 60?
A) 0.2271
B) 0.3729
C) 0.8929
D) D)-1.14
E) 0.0764

Question

Quizplus · Accepted Answer

To find the number of students who scored less than 60, we first calculate the z-score for a score of 60. 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 $z = \frac{(60 - 70)}{7} = -1.43$. Looking up -1.43 on the standard normal distribution table gives us approximately 0.0764. This value represents the proportion of students who scored less than 60. Since there are 100 students, approximately 7.64 students scored less than 60, but the question asks for the proportion, so the correct answer is 0.0764.

The Average Score of 100 Students Taking a Statistics Final