Question

1. 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? (a) 19 and 21 (b) 15 and 20 (c) 20 and 20 (d) 15 and 25 (e) 10 and 30

Explanation:

Step1: Recall the Empirical Rule

The Empirical Rule for a normal - distribution states that 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 $\mu = 20$ (mean) and $\sigma = 5$ (standard deviation). So, $20 - 5=15$.

Step3: Calculate the upper bound

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

Answer:

D. 15 and 25