Suppose an electronics manufacturer knows from previous data that 1% of

one type of an electronic component are defective. The quality control

inspector randomly selects components until a defective one is found. Is this

a binomial experiment? Why or why not?

It is not a binomial experiment

Step-by-step explanation:

For an experiment to be a binomial, the variable associated with the experiment has to be a binomial random variable.

A binomial random variable should satisfy the following conditions:

1. There should be a fixed known number of trials.

2. There should be only 2 outcomes of a trial i. e. either success or failure

3. Trial results should be independent

4. Same probability for each trial success or failure

The Random variable in this experiment is X = no. of selections until a defective one is found.

Now here, X does not satisfy the first condition for a binomial variable itself as the no. of trials is not fixed and is unknown.

Hence X is not a binomial random variable.

So this experiment is not binomial experiment.

It is not a binomial experiment because the random variable associated with this experiment is a Geometric random variable.

Step-by-step explanation:

For an experiment to be a binomial experiment the variable associated with the experiment has to be a binomial random variable.

A binomial random variable should satisfy the following conditions:

There should be a fixed known no. of trials There should be only 2 outcomes of a trial i. e either success or failure Trial results should be independent Same probability for each trial success or failure

Now lets see what is the random variable in this experiment:

The Random variable would be X = no. of selections until a defective one is found.

X does not satisfy the first condition for a binomial variable itself as the no. of trials is not fixed and is unknown.

Hence X is not a binomial random variable.

Rather X is a Geometric random variable. If we consider finding a defective one as a success then the variable is defined as the no. of trials until a success is achieved. But a binomial random variable is defined by no. of successes in a fixed no. of trials.

Hence it is not a binomial experiment.