Question

For a certain type of hay fever, Medicine H has a 30% probability of working.

In which distributions does the variable X have a binomial distribution?

Select EACH correct answer.




A. When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.

B. When the medicine is tried with six patients, X is the number of patients for whom the medicine does not work.

C. When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.

D. When the medicine is tried with two patients, X is the number of doses each patient needs to take.

Answer 1

Explanation:

In the first three, the probability of success (or failure) is constant, so those distributions have binomial distributions.

The problem says nothing about doses, which most likely wouldn't be independent events anyways.

So the answer is indeed the first three. Good job!

Answer 2

Answer: A . When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.

B. When the medicine is tried with six patients, X is the number of patients for whom the medicine does not work.

C. When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.

Explanation:

• A binomial distribution is a frequency distribution of the possible number of successful outcomes in a given number of trials having same probability of success .

From all the given options, option A, B and C has trials that have same probability of success for the given event X .

But option D shows event X is the number of doses each patient needs to take which varies depending on the patient.

Hence, the trials do not have same probability of success .