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Which one of the following  is likely to be well described by a Binomial model?Group of answer choicesThe number of accidents in a large factory during one 8-hour shiftThe number of spades in a bridge hand (ie a random selection of 13 cards from a pack of 52 cards)The number of tosses of a fair coin until the 10th head is obtainedThe number of years between floods at a certain locationThe number of apples that are 'infected' in a sample of 40 apples randomly selected from a large consignment of apples.

Question

Which one of the following  is likely to be well described by a Binomial model?Group of answer choicesThe number of accidents in a large factory during one 8-hour shiftThe number of spades in a bridge hand (ie a random selection of 13 cards from a pack of 52 cards)The number of tosses of a fair coin until the 10th head is obtainedThe number of years between floods at a certain locationThe number of apples that are 'infected' in a sample of 40 apples randomly selected from a large consignment of apples.

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Solution

A binomial model is appropriate when the following conditions are met:

  1. The number of observations n is fixed.
  2. Each observation is independent.
  3. Each observation represents one of two outcomes ("success" or "failure").
  4. The probability of "success" p is the same for each observation.

Given these conditions, let's evaluate each of the options:

  1. The number of accidents in a large factory during one 8-hour shift: This is not binomial because the number of potential accidents is not fixed and the probability of an accident is not constant.

  2. The number of spades in a bridge hand (i.e., a random selection of 13 cards from a pack of 52 cards): This is not binomial because the draws are not independent (once a card is drawn, it changes the composition of the deck).

  3. The number of tosses of a fair coin until the 10th head is obtained: This is not binomial because the number of trials is not fixed (it continues until the 10th head appears).

  4. The number of years between floods at a certain location: This is not binomial because the number of years is not fixed and the probability of a flood is not constant.

  5. The number of apples that are 'infected' in a sample of 40 apples randomly selected from a large consignment of apples: This could be a binomial distribution. The number of trials is fixed (40 apples), each apple is either infected (success) or not (failure), and if the consignment of apples is large enough, the probability of an apple being infected is roughly constant.

Therefore, the correct answer is "The number of apples that are 'infected' in a sample of 40 apples randomly selected from a large consignment of apples."

This problem has been solved

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