Question

given the mean of a data set is 131 and the standard deviation is 8, where will about 68% of the data lie? 131 to 139 123 to 139 123 to 131

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 1 standard deviation. Let the mean $\mu = 131$ and the standard deviation $\sigma=8$. The lower bound $L=\mu - \sigma=131 - 8=123$.

Step3: Calculate the upper bound

The upper bound is the mean plus 1 standard deviation. The upper bound $U=\mu+\sigma = 131 + 8=139$.

Answer:

123 to 139