Question

The mean number of points in 1977 was 1189 points with standard deviation of 397 points. With a roughly normal distribution, what percent of performances would fall between 395 and 1983 points?

Your answer
A. 100%
B. 68%
C. 95%
D.99.7%

Answer 1

C. 95%

Explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 1189 points, standard deviation of 397 points.

Percentage between 395 and 1983 points?

395 = 1189 - 2*397

1983 = 1189 + 2*397

So within 2 standard deviations of the mean, which by the Empirical Rule is approximately 95%, and the answer is option C.