Binomial Distribution

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Presentation transcript:

Binomial Distribution Situations often arise where success or failure are the only options, such situations result in a binomial distribution. To use the binomial distribution the following conditions must apply: F the number of trials must be fixed I each trial must be independent of the other S the probability of success at each trial must be the same T there are only two outcomes, success or failure

We use the parameters n,π and x for the binomial distribution n is the number of trials conducted x is the total number of successes in n trials π is the probability of success for each trial 1-π is the probability of failure If all the conditions are met then the following binomial distribution formula can be used to find probabilities We use the parameters X~B(n,π) P(X=x)= 0≤x≤n xεW

eg. Traffic experts have determined that 1% of all drivers do not wear seatbelts. If ten motorists are stopped at one particular intersection , what is the probability that One motorist stopped is not wearing a seatbelt. X~B(10,0.01) NB P(failure)=1-0.01 = 0.99 P(X=1)= = = (0.01)(0.99)9 = 0.09135 (4sf)

X~B(10,0.01) ie the probability of 0 successes P(X=0) = = (ii) All people stopped are wearing seatbelts ie the probability of 0 successes X~B(10,0.01) P(X=0) = = = 1×1×(0.99)10 = 0.9044 (4sf)

No more than one of the drivers who are stopped are not wearing a seatbelt P(X≤1) =P(X=1)+P(X=0) =0.09135 + 0.9044 = 0.9958 (4sf)