Question

the probability that a randomly selected visitor to a certain website will be asked to participate in an online survey is 0.40. avery claims that for the next 5 visitors to the site, 2 will be asked to participate in the survey. is avery interpreting the probability correctly? a yes, because 2 out of 5 is equal to 40%. b yes, because participants in the survey are selected at random. c no, because there could be voluntary response bias. d no, because only 40% of all people will visit the site. e no, because 0.40 represents probability in the long run over many visits to the site.

Explanation:

Probability represents the long - term relative frequency. A probability of \(0.40\) (or \(40\%\)) for being asked to participate in the survey means that over a large number of visitors (in the long run), about \(40\%\) will be asked. For a small sample of \(n = 5\) visitors, the actual number of visitors asked to participate can vary. It is not guaranteed that exactly \(2\) out of \(5\) will be asked.

• Option A: Just because \(\frac{2}{5}=0.4\) (or \(40\%\)) in a small sample of \(n = 5\), it doesn't mean that this is how probability works. Probability is about the long - run behavior, not a fixed outcome for a small number of trials.
• Option B: The fact that participants are selected at random does not justify the claim that exactly \(2\) out of \(5\) will be asked. Random selection and probability in the long run are different concepts in this context.
• Option C: Voluntary response bias is not relevant to the misinterpretation of probability here. The issue is about the nature of probability (long - run vs. short - run) not about bias in responses.
• Option D: The statement “only \(40\%\) of all people will visit the site” is not related to the misinterpretation of the probability of being asked to participate in the survey.
• Option E: This is correct. Probability \(p = 0.40\) is a long - run proportion. For a small number of trials (\(n=5\) visitors), the actual number of “successes” (being asked to participate) is not fixed.

Answer:

E. No, because \(0.40\) represents probability in the long run over many visits to the site.