Question

Which of the following statements from the empirical rule is correct?

a) 68% of the data lies within one standard deviation of the mean
b) 95% of the data lies within two standard deviations of the mean
c) 99.7% of the data lies within three standard deviations of the mean
d) All of the above

Answer 1

The Empirical Rule states that for a normal distribution, approximately 68%, 95%, and 99.7% of data lie within one, two, and three standard deviations from the mean, respectively. Option (d) 'All of the above' is correct as it includes all these statements.

Step-by-step explanation:

The question relates to the Empirical Rule which is a statistical rule stating the percentages of data that fall within certain standard deviations from the mean in a normal distribution. The statements given adhere to the percentages that are commonly found in bell-shaped distributions:

1. About 68% of data lies within one standard deviation of the mean.
2. About 95% of data lies within two standard deviations of the mean.
3. About 99.7% of data lies within three standard deviations of the mean.

All these statements are indeed part of the Empirical Rule. Therefore, the correct answer which encompasses all these statements is option (d) All of the above.