Question

find the margin of error for the given values of c, σ, and n.
c = 0.90, σ = 3.3, n = 36
click the icon to view a table of common critical values.
e = (round to three decimal places as needed.)

Explanation:

Step1: Find the critical value \( z_{\alpha/2} \)

For \( c = 0.90 \), \( \alpha=1 - c=1 - 0.90 = 0.10 \). Then \( \alpha/2=\frac{0.10}{2}=0.05 \).
From the standard normal table (or common - critical - values table), \( z_{\alpha/2}=z_{0.05} = 1.645 \).

Step2: Calculate the margin of error \( E \)

The formula for the margin of error when the population standard deviation \( \sigma \) is known is \( E = z_{\alpha/2}\frac{\sigma}{\sqrt{n}} \).
Given \( \sigma = 3.3 \), \( n = 36 \), and \( z_{\alpha/2}=1.645 \).
Substitute the values into the formula: \( E=1.645\times\frac{3.3}{\sqrt{36}} \).
Since \( \sqrt{36}=6 \), then \( E = 1.645\times\frac{3.3}{6} \).
First, calculate \( \frac{3.3}{6}=0.55 \).
Then \( E=1.645\times0.55 \).
\( E = 0.90475\approx0.905 \)

Answer:

\( 0.905 \)