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A veterinarian is using a new vaccine for cats. The vaccine has a 10% probability of causing side effects.

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

Select each correct answer.



When the vaccine is given to three cats, X is the number of cats that have side effects.

When the vaccine is given to multiple cats, X is the total number of cats that receive the vaccine.

When the vaccine is given to multiple cats, X is the number of cats that receive the vaccine until one of them has side effects.

When the vaccine is given to six cats, X is the number of cats that do not have any side effects.

Respuesta :

Blitztiger
The first and fourth options are binomial distributions, since the 3 or 6 cats will either have or not have side effects.

The second option is not even a distribution, as you would know the exact number who received the vaccine.
The third option is not a binomial distribution, as you have set the # of cats (1) who will have side effects, rather than the number of cats to be tested.
astultz309459

Answer:

When the vaccine is given to multiple cats, X is the total number of cats that receive the vaccine

Step-by-step explanation:

The first and fourth options are binomial distributions, since the 3rd or 6th cat will either have or not have side effects.


The second option is not even a distribution, as you would know the exact number who received the vaccine.

The third option is not a binomial distribution, as you have set the # of cats who will have side effects, rather than the number of cats to be tested.

So for the random variable X ,where X is the total number of cats that receive the vaccine. We have the binomial distribution for probability of causing side effect denoted by

p = 10% =0.1

and probability of not causing side effect denoted by

q = 1-0.1 =0.9

Then  probability function for random variable X is where n is total number of cats.

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