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1 - Binomial Probability Distributions Definition Distribution. The procedure must have a fied number of trials.. The trials must be independent. (The outcome of any individual trial doesn t affect the probabilities in the other trials.). Each trial must have all outcomes classified into two categories.. The probabilities must remain constant for each trial. Notation for Distributions n = fied number of trials = specific number of in n trials p = probability of success in one of n trials q = probability of failure in one of n trials (q = - p ) = probability of getting eactly success Be sure that and p both refer to the same category being called a success.
2 Probability Distribution Number of Girls Among Fourteen Newborn Babies Method Method n! (n - )!! = p q n-
3 Method n! (n - )!! = p q n- = n C p q n- for calculators with n C r key, where r = Eample: Find the probability of getting eactly correct responses among different requests from AT&T directory assistance. Assume in general, AT&T is correct % of the time. This is a binomial eperiment where: n = = p =. q =. Eample: Find the probability of getting eactly correct responses among different requests from AT&T directory assistance. Assume in general, AT&T is correct % of the time. This is a binomial eperiment where: n = = p =. q =. Using the binomial probability formula to solve: P() = C.. =.
4 Method Table A- in Appendi A For n = and p =. Table A- n For n = and p =. Table A- n
5 For n = and p =. Table A- Distribution n Eample: Using Table A- for n = and p =., find the following: a) The probability of eactly b) The probability of at least a) P() =. b) P(at least ) = P( or or ) = P() or P() or P() = =. Method Using Technology STATDISK Minitab Ecel TI-/
6 n! = (n - )!! p q n- Number of outcomes with eactly = n C r Number of outcomes with eactly p q n- = n C r p q n- Number of outcomes with eactly Probability of for any one particular order
7 Eample Nine percent of men and.% of women cannot distinguish between red and green. This is the type of color blindness that causes problems with traffic signals. If si men are randomly selected for a study of traffic signal perceptions, find the probability that eactly two of them cannot distinguish between red and green.
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