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 theU.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.

On average$\left(\mu \right),$ how many would you expect to answer yes?

Short answer

The average number of freshmen answering yes is$5.{704}^{~}5$.

Step-by-step solution

Given information

$$\begin{gathered} \text{Samplesize,}n=8 \\ \text{Theporportionofstudentswhosaidyestohavetherighttolegalmartialstatus}=71.3\% \end{gathered}$$

Explanation

The average number of students who would answer yes is calculated by

$\mu =np$

wherenis the number of trials andpis the probability of success.

$p=0.713$

localid="1649834849613" $$\begin{gathered} \mu =8*0.713 \\ =5.704 \\ \approx 5 \end{gathered}$$

As a result, the predicted number of freshmen who say yes is $5.704$, which is roughly equal to$5$.