Question

You also mentioned that σ=80 and n=100. To find the margin of error for a 99.7% confidence interval, you can use the formula xˉ±z∗σ​/n​. Please provide the answer.

Answer 1

The margin of error for a 99.7% confidence interval is approximately
`\( \pm (2.576 * 80)/(√(100)) \)`.

Step-by-step explanation:

To find the margin of error for a confidence interval, we use the formula
`\( \text{margin of error} = z^* * (\sigma)/(√(n)) \)`. In this case, for a 99.7% confidence interval, the critical z-value is approximately 2.576 (obtained from standard normal distribution tables).

Substitute the given values:
`\( z^* = 2.576 \), \( \sigma = 80 \),` and \( n = 100 \) into the formula. Calculate to get the margin of error.

The margin of error represents the range within which the true population mean is likely to fall. A higher confidence level results in a wider margin of error.