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: 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,
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