Questions: Use the confidence interval to find the margin of error and the sample mean. (1.58,1.92) The margin of error is (Round to two decimal places as needed.)

Solution Steps

To find the margin of error and the sample mean from a confidence interval, we can use the following steps:

1. The sample mean is the midpoint of the confidence interval.
2. The margin of error is half the width of the confidence interval.

The sample mean \( \bar{x} \) is calculated as the midpoint of the confidence interval. Given the lower bound \( 1.58 \) and the upper bound \( 1.92 \), we find:

\[ \bar{x} = \frac{1.58 + 1.92}{2} = 1.75 \]

The margin of error \( E \) is half the width of the confidence interval. The width is given by the difference between the upper and lower bounds:

\[ E = \frac{1.92 - 1.58}{2} = 0.17 \]

Final Answer