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In a binomial experiment, the probability of a success in each trial is 0.6.
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If 25 trials are performed, what is the median?
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Any binomial experiment has parameters 𝑛 and 𝑝, where 𝑛 is the number of trials and 𝑝 is the probability of success.
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In this question, there were 25 trials.
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Therefore, 𝑛 is equal to 25.
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The probability of success in each individual trial was 0.6.
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Therefore, 𝑝 is equal to 0.6.
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We can therefore write the binomial distribution in this case as follows.
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The mean or 𝐸 of 𝑥 for any binomial experiment is calculated by multiplying 𝑛 by 𝑝.
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In this case, we need to multiply 25 by 0.6.
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This is equal to 15.
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Therefore, the mean is 15.
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The expected numbers of success over 25 trials is 15.
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We were asked to work out the median.
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In general, there is no single formula to find the median for a binomial distribution.
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However, if our value for 𝑛𝑝 is an integer or whole number, then the mean median and mode all equal 𝑛𝑝.
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This means that, in this example, when the mean is equal to 15, the median will also be equal to 15.
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A binomial experiment with 25 trials and probability of success equal to 0.6 has a median of 15.