Question

Use the following information to answer the next eight exercises: The Higher Education Research Institute at UCLA collected data from $203,967$incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. $71.3\%$ of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly pick eight first-time, full-time freshmen from the survey. You are interested in the number that believes that same sex-couples should have the right to legal marital status.

What is the standard deviation$\left(\sigma \right)$?

Short answer

The standard deviation (s) is$1.2795$.

Step-by-step solution

Given information

$$\begin{gathered} n=8 \\ p=1-0.713 \\ =0.287 \end{gathered}$$

Explanation

Standard deviation is calculated as:

$$\begin{gathered} \sigma =\sqrt{npq} \\ =\sqrt{np\left(1-p\right)} \end{gathered}$$

Heren is the number of trials,

p is the probability of success,

$q\left(1-p\right)$is the probability of failure.

$$\begin{gathered} \sigma =\sqrt{8*0.713*0.287} \\ =1.2795 \end{gathered}$$

As a result, the distribution's standard deviation is$1.2795$