The mean of a binomial distribution is calculated using the formula:
μ = n * p
Where:
- μ is the mean of the distribution.
- n is the number of trials.
- p is the probability of success on each trial.
In a binomial distribution, we are dealing with a specific number of independent trials, each with two possible outcomes—success or failure. The probability of success is denoted by p, while the probability of failure is 1 – p.
The mean gives us the expected number of successes in n trials. For example, if you were flipping a coin 10 times (where getting heads is considered a success), and the probability of getting heads on each flip is 0.5, the mean number of successes would be:
μ = 10 * 0.5 = 5
This means that out of 10 flips, you would expect to get heads 5 times, on average. Understanding the mean in a binomial distribution can help in various practical applications, such as quality control and risk assessment.