# How to use the BINOM.INV function

**What is the BINOM.INV function?**

The BINOM.INV function calculates the minimum value for which the cumulative binomial distribution is equal to or greater than a given threshold value.

The BINOM.INV function was introduced in Excel 2010 and has replaced the outdated CRITBINOM function.

#### Table of Contents

## 1. Introduction

**What is the difference between the BINOM.INV function and the BINOM.DIST function?**

BINOM.INV(*trials,probability_s,alpha*)

BINOM.DIST(*number_s,trials,probability_s,cumulative*)

**What is the binomial distribution probability?**

The binomial distribution probability gives the likelihood of a specific number of successes occurring in a fixed number of independent trials, each having the same binary success/failure probability.

**What is an independent trial in terms of binomial distribution?**

An independent trial in the context of the binomial distribution refers to each individual test or instance having two possible outcomes, success or failure, in which the result of one trial does not affect the probability of success in subsequent trials.

**What i****s a ****binary success/failure probability?**

A binary success/failure probability describes two mutually exclusive possible outcomes of a trial, conventionally labeled as "success" with probability p and "failure" with probability 1-p, that sum to 1, like heads or tails on a coin flip.

**What is binomial?**

The binomial is a discrete probability distribution that models the number of successes in a fixed number of independent trials, each with a binary success/failure outcome and a constant success probability across trials.

**What is a distribution in statistics?**

A distribution in statistics refers to a function representing the frequencies of different potential outcomes for a random variable or dataset, summarized visually in a histogram or mathematically with a probability distribution function.

## 2. BINOM.INV function Syntax

BINOM.INV(*trials,probability_s,alpha*)

## 3. BINOM.INV function Arguments

trials |
Required. How many Bernoulli trials. |

probability_s |
Required. The probability of success in each test. |

Alpha |
Required. The threshold value. |

**What are Bernoulli trials?**

Bernoulli trials are random experiments with binary outcomes labeled success or failure that remain constant across trials and are independent, meaning the result of one trial does not affect the next, named after Swiss mathematician Jakob Bernoulli.

## 4. BINOM.INV Function Example 1

**The probability that a customer accepts an offer is estimated to be 70%. The offer is given to 30 customers. How many of them accepts the offer if alpha (probability value) is 0.5?**

The inverse binomial distribution is what we need to calculate the number of customers that accepts the offer. It calculates the minimum value for which the cumulative binomial distribution is equal to or greater than a given threshold value which is 0.5 (50%) in this example shown in cell C16 in the image above.

The number of trials is the total number of customers, cell C17 contains 30 meaning there are 30 customers.

In other words, alpha is the probability value for which you want to find the smallest value of x. Each trial has the same probability of success (0.7 or 70%) meaning 70% is the probability a customer accepts the offer. The probability value i specified in cell C18 displayed in cell C18 in the image above.

Formula in cell C8:

The formula returns 21. This means that the smallest number of customers who accept the offer (x) for which the cumulative probability of getting x or fewer customers accepting the offer is greater than or equal to 0.5 (or 50%) is 21. If the probability value (alpha) is 0.5, at least 21 out of the 30 customers will accept the offer.

We can check the value 21 using the BINOM.DIST function and calculate the probability (alpha) value.

The BINOM.DIST function above returns approx. 0.568 (56.8%) for 21 customers. 20 customers returns 0.411 (41.1%) 21 customers satisfies the alpha condition equal to 0.5 (50%) or larger.

The chart in the image above shows an orange line representing the cumulative probability. Go to 0.7 on the secondary y-axis to the right and find the value of x that intersects. The x-axis shows 21 which seems to match the calculated number 21.

## 5. BINOM.INV Function Example 2

**There are 15 machines that operate independently of each other in a factory. The probability of a breakdown occurring during a day is 0.2 for each of the machines. How many machines will stop during a certain day if alpha is 0.8 (probability)?**

The inverse binomial distribution lets you calculate the number of machines that breaks down based on a independent probability of 0.2 (20%), a total of 15 machines (trials) and alpha (probability) is 0.8 or 80%.

The probability_s argument is specified in cell C18, trials argument is given in cell C17, and the alpha argument is in cell C16.

The formula returns 4. This means that the smallest number of machines that break down during a certain day for which the cumulative probability is greater than or equal to 0.8 (or 80%) is 4.

We can check the value 4 using the BINOM.DIST function and calculate the probability (alpha) value.

The BINOM.DIST function above returns approx. 0.836 (83.6%) for 4 machines. 3 machines return 0.648 (64.8%). 4 machines satisfies the alpha condition equal to 0.8 (80%) or larger.

## 6. BINOM.INV Function Example 3

**There are 25 students in a class. There is a 40% risk that each student, independently of each other, will catch a harmless but highly contagious cold. How many will attend school on the same day if the alpha is 0.95 (95%)?**

Arguments

: total number of students in the class: 25 (cell C17)*trials*: Probability of catching the cold for each student (probability of success): 0.4 or 40% (cell C18)*probability_s*: The probability value (α) is 0.95 or 95% (cell C16)*alpha*

We want to find the smallest value of x (the number of students who will not catch the cold) for which the cumulative binomial probability is greater than or equal to 0.95.

Formula in cell C21:

BINOM.INV(25,0.4,0.95) returns 14 students that will catch the cold. 25 -14 equals 11 students who will not catch the cold.

The image above shows a chart, 0.95 on the secondary y-axis (to the right) matches value 14 on the x-axis.

## 7. BINOM.INV function not working

The BINOM.INV function returns

- #VALUE! error value if
*any*argument is non-numeric. - #NUM! error value if:
*trials*< 0 (zero)*probability_s*< 0 (zero)*alpha*< 0 (zero)*alpha*> 1

### Functions in 'Statistical' category

The BINOM.INV function function is one of 73 functions in the 'Statistical' category.

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