Question

find the margin of error for the given values of c, σ, and n.
c = 0.90, σ = 3.4, 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 \( z_{\alpha/2} \)

Given \( c = 0.90 \), then \( \alpha=1 - c=1 - 0.90 = 0.10 \). So \( \alpha/2=\frac{0.10}{2}=0.05 \).
From the standard normal 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 \( E = z_{\alpha/2}\frac{\sigma}{\sqrt{n}} \).
Substitute \( z_{\alpha/2}=1.645 \), \( \sigma = 3.4 \), and \( n = 36 \) into the formula:
\( E=1.645\times\frac{3.4}{\sqrt{36}} \)
Since \( \sqrt{36}=6 \), then \( E = 1.645\times\frac{3.4}{6} \)
\( E=1.645\times0.5666\cdots\)
\( E\approx0.932 \)

Answer:

\( 0.932 \)