Problem

The following confidence interval gives a range of likely values for the average commute distance of all students attending class at the Okeechobee campus of IRSC.
\[
(14.4,18.8)
\]

Determine the point estimate $(\bar{x})$ and margin of error $(E)$ used to construct this particular confidence interval.
\[
\begin{array}{l}
\bar{x}=\square \\
E=\square
\end{array}
\]

Answer

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Answer

Final Answer: The point estimate $\bar{x}$ is \(\boxed{16.6}\) and the margin of error $E$ is \(\boxed{2.2}\).

Steps

Step 1 :The problem provides a confidence interval for the average commute distance of all students attending class at the Okeechobee campus of IRSC, which is (14.4,18.8).

Step 2 :We are asked to determine the point estimate $(\bar{x})$ and margin of error $(E)$ used to construct this particular confidence interval.

Step 3 :The point estimate is the average of the lower and upper bounds of the confidence interval. So, we calculate it as \(\bar{x} = \frac{{14.4 + 18.8}}{2} = 16.6\).

Step 4 :The margin of error is the difference between the upper bound and the point estimate. So, we calculate it as \(E = 18.8 - 16.6 = 2.2\).

Step 5 :Final Answer: The point estimate $\bar{x}$ is \(\boxed{16.6}\) and the margin of error $E$ is \(\boxed{2.2}\).

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