Question

The mean of a normally distributed dataset is 12, and the standard deviation is 2.
____% of the data points lies between 8 and 16.

Answer 1

The mean is 12 and the standard deviation is 2

Notice: mean + 2(standard deviation) = 12 + 2(2) = 16

Mean - 2(standard deviation) = 12 - 2(2) = 8

So the boundaries 8 and 16 represent +/- 2 standard deviations from the mean

Looking at the normal distribution curve, what % of values are within 2 standard deviations of the mean? See attached.

https://i0.wp.com/statisticsbyjim.com/wp-content/uploads/2021/08/empirical_rule_graph2.png?fit=572%2C384&ssl=1

Answer 2

Review the empirical rule

By definition 95% of the data lies within 2 standard deviations of the mean.