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3 Coin Toss Probability Distribution# of HeadsProbabilityBinomial Distribution– used when probability problem can be reduced to 2 possible independent outcomes, fixed # of trials, probability of success remains the same for each trialNotationP(s) – probability of successP(f) – probability of failurep – numerical probability of successq – numerical probability of failuren – number of trialsX – number of successesP(S)=p, P(F)=q=1–pP(X) = nCx× px× qn-xmean=μ=npvariance=σ2=npqstandard deviation=σ=√npq
Info About Decks of Cards52 total cards, 4 suits – hearts (red), diamonds (red), clubs (black), spades (black), each with 13 cardsCards in each suit: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, KingNormal Distribution:Bell-shapedUnimodalMed=Mode=Meantotal area under curve=100%Follows Empirical Rule: for a normal distribution, nearly all of the data will fall within three standard deviationsof the mean. 68% of data falls w/in 1 standard deviation from the mean95% fall w/in 2 99.7% fall w/in 3Chapter 6: Central Limit TheoremCentral Limit Theorem– As the sample size increases, the shape of the distribution of the sample means taken with replacement from a population with mean μ and standard deviation σwill approach a normal distribution. Standard deviation of sample means is called the standard error of the mean. Used for groups, e.g. Find the probability that 100 women… *If the sampleis greater than 30, don’t need to test for normality.Examples