To calculate the margin of error (ME) at a 95% confidence level, we can use the formula:
\[ ME = z \times \frac{\sigma}{\sqrt{n}} \]
where:
- \( z \) is the z-value corresponding to the desired confidence level,
- \( \sigma \) is the population standard deviation,
- \( n \) is the sample size.
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Determine the z-value for a 95% confidence level: For a 95% confidence level, the z-value (which you can find in the z-table) is approximately 1.96.
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Identify the given values:
- Population standard deviation (\( \sigma \)) = 20 minutes
- Sample size (\( n \)) = 100
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Calculate the standard error (SE):
\[ SE = \frac{\sigma}{\sqrt{n}} = \frac{20}{\sqrt{100}} = \frac{20}{10} = 2 \]
- Calculate the margin of error (ME):
\[ ME = z \times SE = 1.96 \times 2 = 3.92 \]
So, the margin of error with a 95% confidence level is 3.92 minutes.