To find the margin of error for a set of data based on its standard deviation and mean, generally, we follow these steps, assuming a common confidence level. Here, we'll use a confidence level of 95%, which is a typical choice for many statistical analyses. This confidence level corresponds to a z-score of 1.96 for a normal distribution.
1. Identify the given data:
- Standard deviation (σ): 9.5
- Mean (µ): 205
2. Choose the z-score corresponding to the desired confidence level:
- For a 95% confidence level, the z-score (z) is 1.96.
3. Calculate the margin of error:
- The formula for the margin of error (ME) using the z-score is:
[tex]\[
\text{Margin of Error} (ME) = z \times \sigma
\][/tex]
- Here, [tex]\(z = 1.96\)[/tex] and [tex]\(\sigma = 9.5\)[/tex].
4. Apply the values to the formula:
- Multiply the z-score by the standard deviation:
[tex]\[
ME = 1.96 \times 9.5 = 18.62
\][/tex]
Therefore, the margin of error is:
[tex]\[
\pm \boxed{18.62}
\][/tex]
