Question

given the mean of a data set is 22 and the standard deviation is 2, where will about 68% of the data lie? 10 to 20 20 to 24 22 to 44

Explanation:

Step1: Recall the empirical rule

For a normal - distributed data set, about 68% of the data lies within 1 standard deviation of the mean.

Step2: Calculate the lower bound

The lower bound is the mean minus the standard deviation. Let $\mu = 22$ be the mean and $\sigma=2$ be the standard deviation. The lower bound $L=\mu - \sigma=22 - 2=20$.

Step3: Calculate the upper bound

The upper bound is the mean plus the standard deviation. The upper bound $U=\mu+\sigma = 22 + 2=24$.

Answer:

20 to 24