Use the confidence interval to find the estimated margin of error. Then find the sample mean.
A store manager reports a confidence interval of $(48.1,79.3)$ when estimating the mean price (in dollars) for the population of textbooks.
The estimated margin of error is
(Type an integer or a decimal.)
Answer
Final Answer: The estimated margin of error is \(\boxed{15.6}\) and the sample mean is \(\boxed{63.7}\).
Step 1 ：The estimated margin of error is calculated as the difference between the upper limit and the lower limit divided by 2. In this case, the upper limit is 79.3 and the lower limit is 48.1. So, the margin of error is \((79.3 - 48.1) / 2\).
Step 2 ：The sample mean in a confidence interval is the midpoint of the interval, which is the average of the upper limit and the lower limit. So, the sample mean is \((79.3 + 48.1) / 2\).
Step 3 ：By calculating, we get the estimated margin of error as \(15.6\) and the sample mean as \(63.7\).
Step 4 ：Final Answer: The estimated margin of error is \(\boxed{15.6}\) and the sample mean is \(\boxed{63.7}\).
