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Binom inv

BINOM.INV Function

The BINOM.INV function in Excel calculates the smallest value for which the cumulative binomial distribution is greater than or equal to a given criterion or probability. In other words, it finds the inverse of the binomial cumulative distribution.

This function is helpful when you need to determine the minimum number of successes required to meet or exceed a target cumulative probability in statistical analyses involving binary outcomes (e.g., success/failure).

Key Features of BINOM.INV:

  • Determines the smallest number of successes for which the cumulative probability reaches or exceeds a specified threshold.
  • Inverse operation of cumulative binomial probability.

Syntax:

BINOM.INV(trials, probability_s, alpha)
  • trials: The total number of independent trials. Must be a positive integer.
  • probability_s: The probability of success on each trial. Must be a number between 0 and 1.
  • alpha: The target cumulative probability. Must be a number between 0 and 1.

Examples:

  1. =BINOM.INV(10, 0.5, 0.8)
    Calculates the smallest number of successes required in 10 trials, where the probability of success for each trial is 0.5, so that the cumulative probability is at least 0.8.
    Result: 6.

  2. =BINOM.INV(15, 0.3, 0.5)
    Finds the smallest number of successes in a series of 15 trials, each with a success probability of 0.3, to reach a cumulative probability of 0.5.
    Result: 5.

  3. =BINOM.INV(8, 0.6, 0.9)
    Determines the minimum number of successes required in 8 trials with a success probability of 0.6 to meet a cumulative probability of 0.9.
    Result: 6.

Notes:

  • If any of the arguments are outside their valid ranges (trials < 1, probability_s not between 0 and 1, alpha not between 0 and 1), the function returns an error (#NUM! or #VALUE!).
  • The function assumes trials are independent, and the probability of success is constant across all trials.
  • BINOM.INV is particularly useful for modeling processes or experiments using the binomial distribution, such as reliability testing, quality control, and risk analysis.

Tip: Use BINOM.INV to back-calculate the required number of successes for meeting a specific target probability.