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 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 select freshman from the study until you find one who replies “yes.” You are interested in the number of freshmen you must ask.

On average (μ), how many freshmen would you expect to have to ask until you found one who replies "yes?"

Short answer

On average, $\mu =1.4025\approx 1$ freshman is expected to be asked until the first who replies 'yes' is found.

Step-by-step solution

Given

Probability of success, $p=71.3\%=0.713$.

Formula used

If a random variable $X$follows a geometric distribution, then the mean $\left(\mu \right)$is given by, $\mu =\frac{1}{p}$

where $p$is that the probability of success.

Calculation

Putting the values in the formula:

$\mu =\frac{1}{0.713}=1.4025$