Question

Use the following information to answer the next six 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 select freshman from the study until you find one who replies “yes.” You are interested in the number of freshmen you must ask.

In words, define the random variable X.

Short answer

When asked if same-sex couples should have the right to legal marital status, the variable X is defined as the number of freshmen selected from the study until the first one replied yes.

Step-by-step solution

Given information

Number of trials, $n=8$

The proportion of students who said yes to have the right to legal marital status $=71.3\%$

Explanation

The random variable is defined as a variable that represents the outcome of interest in a random experiment and is denoted by upper case alphabets. $X$is the number of freshmen who were randomly chosen from the study till the first one said "yes" when asked if same-sex couples should be allowed to marry legally.$X$is a discrete random variable since it can only take a finite number of values.