To determine the margin of error, we'll assume a 95% confidence level. For a 95% confidence interval, the corresponding Z-value is typically 1.96.
1. Identify the given standard deviation:
- The standard deviation of the population is 1.9.
2. Identify the Z-value for the desired confidence interval:
- For a 95% confidence level, the Z-value is 1.96.
3. Calculate the margin of error:
- Margin of error (E) is given by the formula:
[tex]\[ E = Z \times \sigma \][/tex]
where [tex]\( Z \)[/tex] is the Z-value and [tex]\( \sigma \)[/tex] is the population standard deviation.
- Plugging in the values:
[tex]\[ E = 1.96 \times 1.9 \][/tex]
4. Perform the multiplication:
- [tex]\( 1.96 \times 1.9 = 3.724 \)[/tex]
Therefore, the margin of error is:
[tex]\[
\pm 3.724
\][/tex]
