Answer:
The margin of error can be calculated using the formula:
\[E = z \times \frac{\sigma}{\sqrt{n}}\]
where \(E\) is the margin of error, \(z\) is the critical value, \(\sigma\) is the population standard deviation, and \(n\) is the sample size.
First, we need to find the critical value corresponding to the confidence level \(c\). For a confidence level of 0.90, the critical value can be obtained from the table of common critical values. Let me go ahead and find it for you.
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Based on the table, for a confidence level of 0.90, the critical value is approximately 1.645.
Now, we can substitute the values into the formula:
\[E = 1.645 \times \frac{3.3}{\sqrt{100}}\]
Calculating this equation:
\[E \approx 1.645 \times \frac{3.3}{10}\]
Simplifying further:
\[E \approx 0.5415\]
Therefore, the margin of error for the given values of \(c = 0.90\), \(\sigma = 3.3\), and \(n = 100\) is approximately 0.542 (rounded to three decimal places).