Question Video: Calculating the Median of a Binomial Distribution

Video Transcript

In a binomial experiment, the probability of a success in each trial is 0.6. If 25 trials are performed, what is the median?

Any binomial experiment has parameters 𝑛 and 𝑝, where 𝑛 is the number of trials and 𝑝 is the probability of success. In this question, there were 25 trials. Therefore, 𝑛 is equal to 25. The probability of success in each individual trial was 0.6. Therefore, 𝑝 is equal to 0.6.

We can therefore write the binomial distribution in this case as follows. The mean or 𝐸 of 𝑥 for any binomial experiment is calculated by multiplying 𝑛 by 𝑝. In this case, we need to multiply 25 by 0.6. This is equal to 15. Therefore, the mean is 15. The expected numbers of success over 25 trials is 15.

We were asked to work out the median. In general, there is no single formula to find the median for a binomial distribution. However, if our value for 𝑛𝑝 is an integer or whole number, then the mean median and mode all equal 𝑛𝑝. This means that, in this example, when the mean is equal to 15, the median will also be equal to 15.

A binomial experiment with 25 trials and probability of success equal to 0.6 has a median of 15.