Question

Construct the probability distribution function (PDF).

Short answer

x	P(x)
0	0
1	0.0009
2	0.0079
3	0.0395
4	0.1227
5	0.2439
6	0.3030
7	0.215
8	0.0667

Step-by-step solution

Given information

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.

Explanation

$\text{Mean}=np=8\left(0.713\right)=5.074$

The value of X is given by $0,1,2,3,4,5,6,7,8$

For each value of X the binomial distribution is given by

$$\begin{gathered} P(x=0)=binompdf(8,0.713,0)=0 \\ P(x=1)=binompdf(8,0.713,1)=0.0009 \\ P(x=2)=binompdf(8,0.713,2)=0.0079 \\ P(x=3)=binompdf(8,0.713,3)=0.0395 \\ P(x=4)=binompdf(8,0.713,4)=0.1227 \\ P(x=5)=binompdf(8,0.713,5)=0.2439 \\ P(x=6)=binompdf(8,0.713,6)=0.3030 \\ P(x=7)=binompdf(8,0.713,7)=0.2150 \\ P(x=8)=binompdf(8,0.713,8)=0.0667 \end{gathered}$$

The results are tabulated as follows:

x	P(x)
0	0
1	0.0009
2	0.0079
3	0.0395
4	0.1227
5	0.2439
6	0.3030
7	0.215
8	0.0667