Question

If a variable has a distribution that is bell-shaped with mean 15 and standard deviation 5 , then according to the Empirical Rule, 68.0% of the data will lie between which values? (This is a reading assessment question. Be certain of your answer because you only get one attempt on this question.) According to the Empirical Rule, 68.0% of the data will lie between __and __.

Answer 1

According to the Empirical Rule, for a bell-shaped distribution (which is approximately normal):

- Approximately 68% of the data falls within one standard deviation of the mean.

- Approximately 95% of the data falls within two standard deviations of the mean.

- Approximately 99.7% of the data falls within three standard deviations of the mean.

Given that the mean is 15 and the standard deviation is 5, you can use this information to find the range within which 68% of the data lies:

- The lower bound: Mean - 1 standard deviation = 15 - 5 = 10

- The upper bound: Mean + 1 standard deviation = 15 + 5 = 20

So, according to the Empirical Rule, 68.0% of the data will lie between 10 and 20.

Explanation: