Question

The mean of the binomial distribution is equal to ________.

1) p
2) np
3) px (1-p)n-x
4) (n) (p) (1-p)

Answer 1

The mean of the binomial distribution is given by the formula np, where n is the number of trials and p is the probability of success per trial.

Step-by-step explanation:

The mean of the binomial distribution is equal to np. This is derived from the properties of a binomial distribution, which is a discrete random variable that results from a series of independent trials, each with two possible outcomes: success or failure. The random variable (X) represents the number of successes in n independent trials, and p is the probability of success in each trial. Given that the probability of failure (q) is 1 - p, the formula for the mean (or expected value) of a binomial distribution is μ = n * p, where n is the number of trials, and p is the probability of success on one trial.