Questions: Suppose we know that a confidence interval is (42, 47.6). Find the error bound and the sample mean. Round to 2 places where possible. a. Mean = b. Error Bound =

Suppose we know that a confidence interval is (42, 47.6). Find the error bound and the sample mean.

Round to 2 places where possible.
a. Mean =
b. Error Bound =

Transcript text: Suppose we know that a confidence interval is (42, 47.6). Find the error bound and the sample mean. Round to 2 places where possible. a. Mean $=$ $\square$ b. Error Bound = $\square$

Solution

Solution Steps

Step 1: Calculate the Sample Mean

The sample mean $ \bar{x} $ is calculated as the average of the lower and upper bounds of the confidence interval:

\[ \bar{x} = \frac{42 + 47.6}{2} = 44.8 \]

Step 2: Calculate the Error Bound

The error bound $ E $ is determined by taking half the difference between the upper and lower bounds of the confidence interval:

\[ E = \frac{47.6 - 42}{2} = 2.8 \]

Final Answer

The results are as follows:

a. Mean $ = 44.8 $
b. Error Bound $ = 2.8 $

Thus, the final boxed answers are:

\[ \boxed{\text{Mean} = 44.8} \] \[ \boxed{\text{Error Bound} = 2.8} \]

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