Question

given the mean of a data set is 48 and the standard deviation is 6, where will about 68% of the data lie? 8 to 24 42 to 54 54 to 60

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 $\mu-\sigma$, where $\mu = 48$ (mean) and $\sigma = 6$ (standard deviation). So, $48 - 6=42$.

Step3: Calculate the upper bound

The upper bound is $\mu+\sigma$. So, $48 + 6 = 54$.
So about 68% of the data lies between 42 and 54.

Answer:

B. 42 to 54