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Construction Engineering 221

Construction Engineering 221. Statistics and Probability Binomial Distribution Part II. Binomial Distribution.

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Construction Engineering 221

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  1. Construction Engineering 221 Statistics and Probability Binomial Distribution Part II

  2. Binomial Distribution • Binomial probability distributions use combination factorials (if order is of no importance, PPPFP) or permutations is order is of importance (PPPPF) to calculate probability of events. • Combinations are just series of permutations. The distribution is used in quality control and other Bernoullian processes

  3. Binomial Distribution • Binomial probability tables (handout) help simplify the analysis • If pass rate is 0.9, may have to find the probability of failure pattern (failure = 0.1) and subtract from one because most binomial tables only go to p = 0.5 • Probability for each pattern of outcomes can be depicted as a tree diagram (Fig 5-3, page 53)

  4. Binomial Distribution • Outcomes can also be shown in tabular form (Table 5-2, page 54) • The mean of a binomial distribution is denoted by µ: µ = n*π, where µ is the expected value of X (in order words, the most common outcome in the distribution), n is the number of trials, and π is the probability success for each independent event

  5. Binomial Distribution • Example- if we flip a coin 10 times, the mean of the binomial probability distribution is 5 (10 * .5)- the “expected value” of number of heads is five • Example from craps table- role of two dice has an expected value of 2(1/36) + 3(2/36)…..11(2/36) + 12(1/36) = 7- which is the number that takes all the money off the board (“crap out”)

  6. Binomial Distribution • The variance of a binomial distribution: Σ(x-μ)2*P(x), or nπ(1-π) 10 flips of a coin has a mean (expected value) of 5 heads with a variance of 10*.5*.5, or 2.5. standard deviation is square root of 2.5, or 1.6

  7. Binomial Distribution Do exercise 14 in class and check answers in back.

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