Statistics 312 11 Binomial Distribution 1 The binomial distribution possesses three essential properties 1 Each elementary event is classified into one of two mutually exclusive and collectively exhaustive categories such as success or failure 2 The probability of an outcome being classified as success p is constant from trial to trial and the probability of an outcome being classified as failure 1 p is constant from trial to trial 3 The outcome success or failure of a particular trial is independent of the outcome on any other trial A binomial random variable X number of successes in a sample of n trials P X x n p n x p 1 x n x p n x Example Suppose a company claims that only 10 of their rechargeable batteries are defective What is the probability that 3 in a package of 4 are defective if the performances of the four are independent p 3 4 1 3 9 1 4 001 9 0036 3 4 3 Statistics 312 11 Binomial Distribution 2 The Mean The mean of a binomial distribution is the product of its two parameters n and p That is x np Example x np 4 10 40 The Standard Deviation The standard deviation of a binomial distribution is Example Read pp 150 156 Prob 4 15 4 17 4 18
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