Question

given the mean of a data set is 400 and the standard deviation is 17, where will about 68% of the data lie? 400 to 417 383 to 417 17 to 400

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 the mean $\mu = 400$ and the standard deviation $\sigma=17$. The lower bound $L=\mu - \sigma=400 - 17 = 383$.

Step3: Calculate the upper bound

The upper bound is the mean plus the standard deviation. The upper bound $U=\mu+\sigma = 400+17=417$.

Answer:

B. 383 to 417