Question
Express the confidence interval (284.5,497.3) in the form of x-bar bar(x) pm ME
Answers
Answered by
GPT-4o mini
To express the confidence interval (284.5, 497.3) in the form of \( \bar{x} \pm ME \), we need to determine the sample mean \( \bar{x} \) and the margin of error \( ME \).
1. **Find the sample mean \( \bar{x} \)**:
\[
\bar{x} = \frac{\text{Lower limit} + \text{Upper limit}}{2} = \frac{284.5 + 497.3}{2} = \frac{781.8}{2} = 390.9
\]
2. **Find the margin of error \( ME \)**:
\[
ME = \frac{\text{Upper limit} - \text{Lower limit}}{2} = \frac{497.3 - 284.5}{2} = \frac{212.8}{2} = 106.4
\]
Now, we can express the confidence interval as:
\[
\bar{x} \pm ME = 390.9 \pm 106.4
\]
Thus, the final expression is:
\[
390.9 \pm 106.4
\]
1. **Find the sample mean \( \bar{x} \)**:
\[
\bar{x} = \frac{\text{Lower limit} + \text{Upper limit}}{2} = \frac{284.5 + 497.3}{2} = \frac{781.8}{2} = 390.9
\]
2. **Find the margin of error \( ME \)**:
\[
ME = \frac{\text{Upper limit} - \text{Lower limit}}{2} = \frac{497.3 - 284.5}{2} = \frac{212.8}{2} = 106.4
\]
Now, we can express the confidence interval as:
\[
\bar{x} \pm ME = 390.9 \pm 106.4
\]
Thus, the final expression is:
\[
390.9 \pm 106.4
\]