The 95% confidence interval for a population mean has a margin of error (E) of 41
The confidence interval for a population mean is given by:
Confidence interval = μ ± E = (μ - E, μ + E)
Where μ is the mean and E is the margin of error.
Since the confidence interval is (428, 510), hence:
μ - E = 428 (1)
μ + E = 510 (2)
Subtracting equation 1 from equation 2:
2E = 82
E = 41
μ - E = 428
μ -41 = 428
μ = 469
Hence the margin of error (E) is 41
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