Question

given the mean of a data set is 42 and the standard deviation is 4, where will about 68% of the data lie? 38 to 42 38 to 46 42 to 46

Explanation:

Step1: Recall empirical rule

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

Step2: Calculate lower bound

The mean $\mu = 42$ and the standard deviation $\sigma=4$. The lower bound is $\mu-\sigma=42 - 4=38$.

Step3: Calculate upper bound

The upper bound is $\mu+\sigma=42 + 4=46$. So about 68% of the data lies between 38 and 46.

Answer:

B. 38 to 46