Find the margin of error for the given values of $\mathrm{c}, \sigma$, and $\mathrm{n}$.
\[
c=0.95, \sigma=3.2, n=64
\]
Click the icon to view a table of common critical values.
$E=\square$ (Round to three decimal places as needed.)
Table of Common Critical Values
\begin{tabular}{c|c}
\begin{tabular}{c}
Level of \\
Confidence
\end{tabular} & $\mathbf{z}_{\boldsymbol{c}}$ \\
\hline $90 \%$ & 1.645 \\
$95 \%$ & 1.96 \\
$99 \%$ & 2.575
\end{tabular}
Answer
\(\boxed{0.784}\) is the margin of error for the given values of c, σ, and n.
Step 1 ：Given values are: confidence level (c) = 0.95, standard deviation (σ) = 3.2, and sample size (n) = 64.
Step 2 ：From the table of common critical values, the critical value (zc) for a 95% confidence level is 1.96.
Step 3 ：The formula to calculate the margin of error (E) is: \(E = zc \times \frac{σ}{\sqrt{n}}\)
Step 4 ：Substitute the given values into the formula: \(E = 1.96 \times \frac{3.2}{\sqrt{64}}\)
Step 5 ：Simplify the expression to find the margin of error (E): \(E = 0.784\)
Step 6 ：\(\boxed{0.784}\) is the margin of error for the given values of c, σ, and n.
