# 3 coin toss probability distribution of heads

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3 Coin Toss Probability Distribution # of Heads Probability Binomial Distribution – used when probability problem can be reduced to 2 possible independent outcomes, fixed # of trials, probability of success remains the same for each trial Notation P(s) – probability of success P(f) – probability of failure p – numerical probability of success q – numerical probability of failure n – number of trials X – number of successes P(S)=p, P(F)=q=1–p P(X) = n C x × p x × q n-x mean=μ=np variance=σ 2 =npq standard deviation=σ=√npq
Info About Decks of Cards 52 total cards, 4 suits – hearts (red), diamonds (red), clubs (black), spades (black), each with 13 cards Cards in each suit: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King Normal Distribution: Bell-shaped Unimodal Med=Mode=Mean total area under curve=100% Follows Empirical Rule : for a normal distribution , nearly all of the data will fall within three standard deviations of the mean . 68% of data falls w/in 1 standard deviation from the mean 95% fall w/in 2 99.7% fall w/in 3 Chapter 6: Central Limit Theorem Central 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 σ will 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 sample is greater than 30, don’t need to test for normality. Examples