Question

Determine whether or not the random variable X is a binomial random

variable.

(a)

X is the number of dots on the top face of a fair die

(b)

X is the number of hearts in a five card hand drawn (without replacement) from a well

shuffled ordinary deck.

(c)

X is the number of defective parts in a sample of ten randomly selected parts coming from a manufacturing process in which 0.02% of all parts are defective.

(d)

X is the number of times the number of dots on the top face of a fair die is even in six rolls of the die.

(e)

X is the number of dice that show an even number of dots on the top face when six dice are rolled at once

(f)

X is the number of black marbles in a sample of 5 marbles drawn randomly and with replacement from a box that contains 25 white marbles and 15 black marbles.

Answer 1

Determine whether or not the random variable X is a binomial random

variable.

(a)

X is the number of dots on the top face of a fair die

This is not a binomial random variable because the individual output for the variable would lies within 1 and 6. Binomial random variable have only two outcomes such as yes or no, success or failure, etc.

(b)

X is the number of hearts in a five card hand drawn (without replacement) from a well

shuffled ordinary deck.

Answer: This is not a binomial random variable, because although each card has outputs as ‘card with heart’ and ‘card without heart’; that is, binomial in nature, but due to without replacement of cards, experiments are not independent.

(c)

X is the number of defective parts in a sample of ten randomly selected parts coming from a manufacturing process in which 0.02% of all parts are defective.

Answer: This is a binomial random variable. The outputs are defective or not defective; binomial in nature. Experiments of drawing parts are independent of each other.

(d)

X is the number of times the number of dots on the top face of a fair die is even in six rolls of the die.

Answer: This is a binomial random variable. The outputs are ‘even’ or ‘odd’. Each roll is independent of other.

(e)

X is the number of dice that show an even number of dots on the top face when six dice are rolled at once

Answer: This is not a binomial random variable. The outputs would range from 0 to 6. Outputs are not binomial in nature.

(f)

X is the number of black marbles in a sample of 5 marbles drawn randomly and with replacement from a box that contains 25 white marbles and 15 black marbles.

Answer: This is a binomial random variable. Outputs are ‘black’ or ‘white’. Marbles are replaced at each time. So, experiments of drawing marbles are independent.