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9 December, 15:01

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?

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Answers (2)
  1. 9 December, 15:07
    0
    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.
  2. 9 December, 15:13
    0
    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.
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