Question

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?

Answer 1

It is not a binomial experiment

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.

Answer 2

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

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:

1. There should be a fixed known no. 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

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 .