Question

Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer. An experimental drug is administered to 200 randomly selected​ individuals, with the number of individuals responding favorably recorded. Does the probability experiment represent a binomial​ experiment?

Answer 1

Answer: Yes, the probability experiment represent a binomial​ experiment

Explanation: The following conditions need to be satisfy for random variable X to follow binomial distribution,

1) There should be fixed number of trials,i.e. n is fixed => Satisfied, there are fixed 200 individuals

2) Each trail must be independent of each other => Satisfied, each individual is independent of each other

3) There should be two possible outcome for each trail, ("Success" or " Failure",  "Yes" or "No"). => Satisfied, there are two outcomes, favorable vs unfavorable.

4) The probability of success, p for each trail should be equality likely. => Satisfied,