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Binom dist

BINOMDIST Function

The BINOMDIST function in Excel calculates the individual term binomial probability for a given number of successes in a set of trials, based on the probability of a single success. In other words, it computes the probability of achieving a specified number of successes in a fixed number of independent trials with the same probability of success.

This function is helpful in statistical analyses, especially in scenarios involving binary outcomes (e.g., success/failure, true/false).

Key Features of BINOMDIST:

  • Evaluates the binomial distribution's probability for a specific number of successes.
  • Can calculate either exact probabilities or cumulative probabilities up to a specified number of successes.

Syntax:

BINOMDIST(number_s, trials, probability_s, cumulative)
  • number_s: The number of successes for which you want to calculate the probability. Must be a non-negative integer.
  • trials: The total number of independent trials. Must be a positive integer.
  • probability_s: The probability of success for each trial. Must be between 0 and 1.
  • cumulative: A logical value (TRUE or FALSE) that specifies whether to calculate cumulative probabilities:
    • If TRUE, BINOMDIST computes the probability of having at most number_s successes.
    • If FALSE, it computes the probability of exactly number_s successes.

Examples:

  1. =BINOMDIST(3, 10, 0.5, FALSE)
    Calculates the probability of exactly 3 successes out of 10 trials, where the probability of success is 0.5. Result: 0.1171875.

  2. =BINOMDIST(2, 5, 0.7, TRUE)
    Computes the cumulative probability of having at most 2 successes out of 5 trials, with a success probability of 0.7. Result: 0.16308.

  3. =BINOMDIST(4, 8, 0.25, FALSE)
    Calculates the probability of exactly 4 successes out of 8 trials, with a success probability of 0.25. Result: 0.033203.

Notes:

  • If any of the arguments are outside their valid ranges (number_s < 0, trials < 1, probability_s not between 0 and 1), the function returns an error (#NUM! or #VALUE!).
  • The BINOMDIST function assumes each trial is independent and that the probability of success remains constant across trials.
  • For cumulative probability calculations, the sum of all probabilities up to number_s is returned.

Tip: Use BINOMDIST for experiments modeled by the binomial distribution, such as quality control, flipping a coin, or testing pass rates.