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.

$X~\_\_\_\_\_(\_\_\_\_\_,\_\_\_\_\_)$

Short answer

The random variable X follows with parameterp, where p is the probability of success and it is denoted as$X-G\left(p\right)i.e.,X~G\left(0.713\right)$.

Step-by-step solution

Given information

Probability of success, $P=71.3\%=0.713$

Explanation

If a freshman answers yes, it is considered a success.

The random variableX is defined as:

X: The number of freshmen chosen from the study until the first one who replies yesis found. It is denoted as:

$$\begin{gathered} X~G\left(P\right) \\ X~G\left(0.713\right) \end{gathered}$$

As a result, we infer that the random variable X has a geometric distribution with parameters. $p=0.713$, i.e., $X~G\left(0.713\right)$.