Question

find the margin of error for the given values of c, σ, and n. c = 0.95, σ = 2.6, n = 36 click the icon to view a table of common critical values. e = (round to three decimal places as needed.) table of common critical values level of confidence $z_c$ 90% 1.645 95% 1.96 99% 2.575

Explanation:

Step1: Identify the critical - value

Since $c = 0.95$, from the table of common critical values, $z_{c}=1.96$.

Step2: Recall the formula for margin of error

The formula for the margin of error $E$ when the population standard - deviation $\sigma$ is known is $E = z_{c}\frac{\sigma}{\sqrt{n}}$. Here, $\sigma = 2.6$ and $n = 36$.

Step3: Substitute the values into the formula

$E=1.96\times\frac{2.6}{\sqrt{36}}$. First, calculate $\sqrt{36}=6$. Then, $\frac{2.6}{6}\approx0.4333$. Finally, $E = 1.96\times0.4333$.
$E=1.96\times0.4333 = 0.849268\approx0.849$.

Answer:

$0.849$