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 values does the random variable $\mathrm{X}$take on?

Short answer

The random variables$\mathrm{X}$has values of$0$to$8$.

Step-by-step solution

Given information

Number of students replied is $71.3\%$.

Number of randomly picked full time freshmen for survey is eight.

Explanation

In binomial distribution $\mathrm{X}$variables have,

Number of trials is eight

Possibility of success$71.3\%$

So,

$\mathrm{X}~\mathrm{B}(\mathrm{t},\mathrm{P})$

$\mathrm{X}~\mathrm{B}(8,0.713)$

So the random variable has trial value of eight,

$\mathrm{X}$Random variable values is ,

$\mathrm{X}=(0,1,2,3,4,5,6,7,8)$