SOLUTION: A random sample of 40 washing machines of a certain brand produced a 95% confidence interval for the mean replacement time of 10.76 to 12.24 years. What is the margin of error of t

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Question 1165662: A random sample of 40 washing machines of a certain brand produced a 95% confidence interval for the mean replacement time of 10.76 to 12.24 years. What is the margin of error of the estimate for the mean of all washing machines of this brand?
Answer by CPhill(2189) (Show Source):
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The **margin of error (ME)** is the half-width of the confidence interval.
You can calculate the margin of error by subtracting the lower bound from the upper bound and dividing the result by two.
$$\text{Margin of Error (ME)} = \frac{\text{Upper Bound} - \text{Lower Bound}}{2}$$
Given the $95\%$ confidence interval is $10.76$ to $12.24$ years:
$$\text{ME} = \frac{12.24 - 10.76}{2}$$
$$\text{ME} = \frac{1.48}{2}$$
$$\mathbf{\text{ME} = 0.74 \text{ years}}$$
The margin of error of the estimate is **0.74 years**.