Final Answer:
The mean (μ) for a binomial distribution with the stated values of n (number of trials) and p (probability of success) is given by the formula μ = n * p.
Step-by-step explanation:
In a binomial distribution, the mean (μ) represents the average number of successes in a given number of trials. The formula for the mean in a binomial distribution is μ = n * p, where n is the number of trials and p is the probability of success on each trial. This formula intuitively makes sense, as the mean is the product of the number of trials and the probability of success.
For example, if we have a binomial distribution with n = 5 trials and p = 0.4 (40% probability of success), the mean (μ) is calculated as 5 * 0.4 = 2. This means, on average, we can expect 2 successes in 5 trials. The mean is a crucial parameter in understanding the central tendency of a binomial distribution.
Understanding and calculating the mean in a binomial distribution is essential in statistical analysis. It provides valuable insights into the expected outcome of a series of independent trials with a fixed probability of success. The mean serves as a measure of central tendency, helping to characterize the distribution and make predictions about the likely number of successes in a given set of trials.