Transcript Prob & binomial dist II

Construction Engineering 221
Statistics and Probability
Binomial Distribution Part II
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
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 53, page 53)
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
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”)
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
Binomial Distribution
Do exercise 14 in class and check answers
in back.