Question

Determine whether or not the random variable X is a binomial random variable. If so, give the values of n and p. If not, explain why not.

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

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 six dice are rolled at once.

Answer 1

it is a binomial probability distributioni if,

there is fixed number of trials, (n)
only two outcomes are there, success and failure (p fixed)
trails are independent of each other              

a)

not binomial ,

as n is not given

....

b)

not binomial,

as it is without replacement (p not fixed)

...........

c)

it is binomial

n = 10

p = 0.02% = 0.0002

...........

d)

it is binomial

n =6

p = 1/2 = 0.5

............

e)

not binomial

as 6 dice are rolled at once

..................

Please revert back in case of any doubt.

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