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Binomial distributions

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Binomial distributions describe experiments with a fixed number (n) of independent trials, where each trial results in one of two possible outcomes (success or failure) with a constant probability (p) of success. The probability of getting exactly k successes in n trials is represented by a binomial probability formula that calculates the number of combinations of k successes from n trials multiplied by the probability of success (p) raised to k and the probability of failure (1-p) raised to n-k.

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BINOMIAL DISTRIBUTIONS GOAL: TO LEARN ABOUT BINOMIAL DISTRIBUTIONS AND SEEING THE SPREAD OF RESULTS

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Binomial distributions

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Binomial distributions

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Binomial Experiments A binomial experiment meets the following conditions: 1. There are n independent trials 2. Each trial has only two possible outcomes, success and failure 3. The probability of success is the same for each trial. This probability is denoted p. The probability of failure is given by 1 – p 4. In the binomial experiment, the probability of exactly k successes in n trials is: ( ) (1 )k n k n kP k successes C p p   

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( ) (1 )k n k n kP k successes C p p    • binomialpdf(#trials, prob p, [, x]) • binomialpdf(n,p,k) • binomialcdf(#trials, prob p, [, x]) • binomialcdf(n,p,k)

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Binomial distributions

  • 1. BINOMIAL DISTRIBUTIONS GOAL: TO LEARN ABOUT BINOMIAL DISTRIBUTIONS AND SEEING THE SPREAD OF RESULTS
  • 4. Binomial Experiments A binomial experiment meets the following conditions: 1. There are n independent trials 2. Each trial has only two possible outcomes, success and failure 3. The probability of success is the same for each trial. This probability is denoted p. The probability of failure is given by 1 – p 4. In the binomial experiment, the probability of exactly k successes in n trials is: ( ) (1 )k n k n kP k successes C p p   
  • 5. ( ) (1 )k n k n kP k successes C p p    • binomialpdf(#trials, prob p, [, x]) • binomialpdf(n,p,k) • binomialcdf(#trials, prob p, [, x]) • binomialcdf(n,p,k)