The mean, μ, and variance, σ 2, for the binomial probability distribution are μ = np and σ 2 = npq. The random variable X = the number of successes obtained in the n independent trials. The outcomes of a binomial experiment fit a binomial probability distribution. This means that for every true-false statistics question Joe answers, his probability of success ( p = 0.6) and his probability of failure ( q = 0.4) remain the same. Suppose Joe always guesses correctly on any statistics true-false question with probability p = 0.6. If a success is guessing correctly, then a failure is guessing incorrectly. For example, randomly guessing at a true-false statistics question has only two outcomes. Another way of saying this is that for each individual trial, the probability, p, of a success and probability, q, of a failure remain the same. Because the n trials are independent, the outcome of one trial does not help in predicting the outcome of another trial.
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