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Find the mean & St. Dev for each. Mean St. Dev X 8 3 Y 12 4 4x ī 7 3x ī 2 y Find the mean & standard deviation x p(x) 4 0.2 7 0.31 12 0.24 15 0.18 18 0.07 BINOMIAL DISTRIBUTION FORMULA Section 6.3A Binomial Experiment - BINS • Binary? • There are two possible outcomes – success and failure • Independent? • Trials must be independent • Number? • The number of trials must be fixed – out of n…. • Success? • On each trial the probability of success must be the same Let E be the event that a person goes out shopping on Black Friday. Find the probability distribution for a sample of 3 people if the P(E) = .78. Probability distribution of going shopping on black Friday for 4 people. P(E) = .78 Let’s Develop the formula! • If I have 5 people, how many ways can I arrange them? đâđâđâđâđ • How many ways can I choose 2 of the 5 who went shopping on black Friday? [đ â đ] â đ â đ â đ đ! = đâđâđ đ−đ ! • But every set of two is the same (SSNNN = SSNNN)… đ! đ!âđ! Binomial Distribution īĻ n īļ x nī x p( x) īŊ ī§ īˇ p q ī¨ xī¸ īĻnīļ n! n Cx īŊ ī§ īˇ īŊ ī¨ x ī¸ (n ī x)! x ! where q īŊ 1ī p The survival rate for a risky operation is 80%. What is the probability that exactly 4 of the next 5 patients survive? USA today stated that 45% of Americans know somebody who became addicted to a drug other than alcohol. If we randomly ask 15 people, what’s the probability that exactly 3 were addicted? What’s the probability that at least 12 are addicted? What the probability that less than 3 are addicted? 90% of the trees planted by a landscaper will survive. If 10 trees are planted, what’s the probability more than eight survive? The probability that a person will subscribe to Statistics Monthly is 48%. Find the probability that out of a group of seven, at least one person subscribes. There are charts as well – but only for some probabilities so you need to know the formula. Homework • Worksheet