Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Survey

Document related concepts

Transcript

The Binomial Distribution Introduction # correct Tally Frequency P(experiment) P(theory) 0 1 2 3 Mix the cards, select one & guess the type. Repeat 3 times per turn and record your results. Introduction # correct Tally Frequency P(experiment) P(theory) 0 1 2 3 4 Repeat guessing 4 times – Graph the results Binomial Formula for theory P(X =x) = nCx x(1 - )n-x • Where n is the number of trials. • is the probability of success. Definition of the Binomial Distribution The Binomial Distribution occurs when: (a) There is a fixed number (n) of trials. (b) The result of any trial can be classified as a “success” or a “failure” (c) The probability of a success ( or p) is constant from trial to trial. (d) Trials are independent. If X represents the number of successes then: P(X =x) = nC x x(1 - )n-x PARAMETERS of binomial distribution Parameters = what describes the distribution ‘n’ Fixed number of trials. ‘’ or ‘p’ The probability of a success. Example #1 a) Flipping a coin 8 times – what is the probability that exactly 3 of them are heads? b) Does this experiment meet the conditions of a binomial distribution? Example #2 Calculate the probability of a drawing pin landing on its back 3 times in 5 trials if the probability of getting a drawing pin to land on its back on any toss is 0.4 Let X be a random variable representing the number of “backs” in 5 tosses of the drawing pin. Then X is binomial with n = 5, = 0.4. We want P(X = 3). (i) By formula: P(X = 3) = (ii) Using tables: P(X = 3) 5C 3 × 0.43 × 0.62 = 0.2304