Question

given the mean of a data set is 20.6 and the standard deviation is 2.2, where will about 68% of the data lie? 18.4 to 20.6 20 to 21 18.4 to 22.8

Explanation:

Step1: Recall the empirical rule

In a normal - distribution, 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 $\mu = 20.6$ and $\sigma=2.2$. The lower bound $L=\mu - \sigma=20.6 - 2.2 = 18.4$.

Step3: Calculate the upper bound

The upper bound is the mean plus the standard deviation. The upper bound $U=\mu+\sigma=20.6 + 2.2=22.8$.

Answer:

18.4 to 22.8