Question

a variable x follows a normal distribution with a mean of 20 and standard deviation of 5. according to the empirical rule, the middle 68% of the data falls between what two x values?
15 and 20
20 and 25
15 and 25
19 and 21

Explanation:

Step1: Recall the Empirical Rule

The Empirical Rule states that for a normal distribution, approximately 68% of the data lies within \(1\) standard deviation (\(\sigma\)) of the mean (\(\mu\)).

Step2: Calculate the lower bound

The lower bound is \(\mu-\sigma\). Given \(\mu = 20\) and \(\sigma=5\), we have \(20 - 5=15\).

Step3: Calculate the upper bound

The upper bound is \(\mu+\sigma\). So, \(20 + 5 = 25\).

Answer:

15 and 25 (the third option)