Question

use the confidence interval to find the margin of error and the sample mean (0.396,0.620) the margin of error is

Explanation:

Step1: Find the sample mean

The sample mean $\bar{x}$ is the mid - point of the confidence interval. The formula for the mid - point of an interval $(a,b)$ is $\bar{x}=\frac{a + b}{2}$.
For the interval $(0.396,0.620)$, we have $\bar{x}=\frac{0.396+0.620}{2}=\frac{1.016}{2}=0.508$.

Step2: Find the margin of error

The margin of error $E$ can be found using the formula $E=\frac{b - a}{2}$.
Substitute $a = 0.396$ and $b = 0.620$ into the formula: $E=\frac{0.620 - 0.396}{2}=\frac{0.224}{2}=0.112$.

Answer:

The margin of error is $0.112$ and the sample mean is $0.508$.