Question

which interval shows 95% of the data given a mean of 15 and a standard deviation of 3? 9 to 21 6 to 24 12 to 18 13 to 16

Explanation:

Step1: Recall the empirical rule

For a normal - distribution, about 95% of the data lies within 2 standard deviations of the mean.

Step2: Calculate the lower bound

The lower bound is $\text{mean}- 2\times\text{standard deviation}$. Given $\text{mean}=15$ and $\text{standard deviation}=3$, the lower bound is $15 - 2\times3=15 - 6 = 9$.

Step3: Calculate the upper bound

The upper bound is $\text{mean}+ 2\times\text{standard deviation}$. So, the upper bound is $15+2\times3=15 + 6=21$.

Answer:

9 to 21