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.)
Transcript text: Use the confidence interval to find the margin of error and the sample mean.
\[
(1.58,1.92)
\]
The margin of error is $\square$
(Round to two decimal places as needed.)
Solution
Solution Steps
To find the margin of error and the sample mean from a confidence interval, we can use the following steps:
The sample mean is the midpoint of the confidence interval.
The margin of error is half the width of the confidence interval.
Step 1: Calculate the Sample Mean
The sample mean xˉ is calculated as the midpoint of the confidence interval. Given the lower bound 1.58 and the upper bound 1.92, we find:
xˉ=21.58+1.92=1.75
Step 2: Calculate the Margin of Error
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=21.92−1.58=0.17
Final Answer
The sample mean is 1.75 and the margin of error is 0.17.