# BINOM.INV

The BINOM.INV function calculates the smallest value for which the cumulative binomial distribution is less than or equal to a specified criteria. This function is commonly used in statistical analysis and probability calculations to determine the probability of a certain number of successful trials in a fixed number of trials.

## Syntax ๐

=BINOM.INV(`Trials`

, `Probability_s`

, `Probability_s`

, `Cumulative`

)

`Trials` | The number of independent trials. |

`Probability_s` | The success probability for each trial. |

`Probability_s` | The criteria probability. |

`Cumulative` | A logical value that determines the form of the function. If TRUE, the BINOM.INV function returns the cumulative distribution function; if FALSE, it returns the probability mass function. |

## About BINOM.INV ๐

In the realm of statistics and probability, when the need arises to pinpoint the smallest number of successful outcomes within a fixed count of independent trials, look no further than the BINOM.INV function in Excel. This formidable tool serves as the cornerstone for computing the probability of achieving a specific number of successes within a designated number of trial runs, catering to a wide array of applications in statistical analysis and decision-making scenarios. Whether it's forecasting the likelihood of successful outcomes in complex experiments or determining the probability of specific event occurrences, BINOM.INV stands as the trusted aide for wielding the power of probability in Excel.

## Examples ๐

Suppose you are conducting 10 independent trials with a success probability of 0.3 for each trial. You want to find the smallest number of successful outcomes such that the cumulative probability is less than or equal to 0.75. The BINOM.INV formula would be: =BINOM.INV(10, 0.3, 0.75, TRUE)

Suppose you are planning 20 independent trials with a success probability of 0.6 for each trial. You aim to ascertain the smallest number of successful outcomes such that the probability mass function is less than or equal to 0.5. The BINOM.INV formula would be: =BINOM.INV(20, 0.6, 0.5, FALSE)

## Notes ๐

The BINOM.INV function assumes that the specified probabilities and the cumulative value are valid and within the range [0,1]. Ensure that the parameters and arguments used in the function align with the specific requirements of your probability calculations and statistical analyses.

## Questions ๐

**How does the BINOM.INV function determine the smallest value of successful outcomes?**

The BINOM.INV function computes the smallest number of successful outcomes by evaluating the cumulative binomial distribution based on the specified criteria probability and the success probability for each trial. It returns the value for which the cumulative distribution is less than or equal to the criteria probability.

**When should I use the TRUE or FALSE option for the Cumulative argument in the BINOM.INV function?**

You should use TRUE for the Cumulative argument when you want the function to return the cumulative distribution function, providing the probability of getting up to the particular number of successful outcomes. On the other hand, using FALSE returns the probability mass function, delivering the probability of getting the exact number of successful outcomes specified.

**Can I use the BINOM.INV function for non-integer values for the number of trials or success probability?**

No, the BINOM.INV function is designed to work with whole number values for the number of trials and the success probability. It is tailored for discrete random variables and does not accommodate non-integer or continuous values.