Problem

The following confidence interval gives a range of likely values for the average height of all American adult women. \[ (58,64) \] Determine the point estimate $(\bar{x})$ and margin of error $(E)$ used to construct this particular confidence interval. \[ \begin{array}{l} \bar{x}= \\ E= \end{array} \]

Solution

Step 1 :Define the lower and upper bounds of the confidence interval as 58 and 64 respectively.

Step 2 :Calculate the point estimate by adding the lower bound and the upper bound and dividing by 2. This gives a point estimate of 61.0.

Step 3 :Calculate the margin of error by subtracting the point estimate from the upper bound. This gives a margin of error of 3.0.

Step 4 :The point estimate $(\bar{x})$ used to construct this confidence interval is 61.0 and the margin of error $(E)$ is 3.0.

Step 5 :So, we have $\bar{x} = \boxed{61.0}$ and $E = \boxed{3.0}$.

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Source: https://solvelyapp.com/problems/p0pR8p70Vd/

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