Provide an appropriate response.
-Three random variables X, Y, and Z, are described below. In which of these situations would it be acceptable to use the binomial distribution?
A: A bag contains 4 blue marbles and 8 red marbles. Five marbles are drawn at random with
Replacement. The random variable X is the number of blue marbles drawn.
B: A bag contains 4 blue marbles and 8 red marbles. Six marbles are drawn at random without
Replacement. The random variable Y is the number of blue marbles drawn.
C: A bag contains 30 blue marbles and 38 red marbles. Three marbles are drawn at random without Replacement. The random variable Z is the number of blue marbles drawn.
A)A only
B)B and C
C)A, B, and C
D)A and C

Question

Provide an appropriate response.
-Three random variables X, Y, and Z, are described below. In which of these situations would it be acceptable to use the binomial distribution?
A: A bag contains 4 blue marbles and 8 red marbles. Five marbles are drawn at random with
Replacement. The random variable X is the number of blue marbles drawn.
B: A bag contains 4 blue marbles and 8 red marbles. Six marbles are drawn at random without
Replacement. The random variable Y is the number of blue marbles drawn.
C: A bag contains 30 blue marbles and 38 red marbles. Three marbles are drawn at random without Replacement. The random variable Z is the number of blue marbles drawn. 
A)A only
B)B and C
C)A, B, and C
D)A and C

Quizplus · Accepted Answer

The binomial distribution is appropriate when each trial is independent and the probability of success is constant. Choice A involves drawing with replacement, which satisfies these conditions. Choices B and C involve drawing without replacement, which means the trials are not independent and the probability of success changes with each draw, making the binomial distribution inappropriate.

Provide an Appropriate Response