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The BINOM.INV function was introduced in Excel 2010 and has replaced the outdated CRITBINOM function.

1. Introduction

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

BINOM.INV finds the number of successes for a given cumulative probability while the BINOM.DIST function calculates probabilities for specific or cumulative successes.

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 is 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. Syntax

BINOM.INV(trials,probability_s,alpha)

3. 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. 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. 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. 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

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

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. 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

7.1 Troubleshooting the error value

When you encounter an error value in a cell a warning symbol appears, displayed in the image above. Press with mouse on it to see a pop-up menu that lets you get more information about the error.

1. The first line describes the error if you press with left mouse button on it.
2. The second line opens a pane that explains the error in greater detail.
3. The third line takes you to the "Evaluate Formula" tool, a dialog box appears allowing you to examine the formula in greater detail.
4. This line lets you ignore the error value meaning the warning icon disappears, however, the error is still in the cell.
5. The fifth line lets you edit the formula in the Formula bar.
6. The sixth line opens the Excel settings so you can adjust the Error Checking Options.

Here are a few of the most common Excel errors you may encounter.

#NULL error - This error occurs most often if you by mistake use a space character in a formula where it shouldn't be. Excel interprets a space character as an intersection operator. If the ranges don't intersect an #NULL error is returned. The #NULL! error occurs when a formula attempts to calculate the intersection of two ranges that do not actually intersect. This can happen when the wrong range operator is used in the formula, or when the intersection operator (represented by a space character) is used between two ranges that do not overlap. To fix this error double check that the ranges referenced in the formula that use the intersection operator actually have cells in common.

#SPILL error - The #SPILL! error occurs only in version Excel 365 and is caused by a dynamic array being to large, meaning there are cells below and/or to the right that are not empty. This prevents the dynamic array formula expanding into new empty cells.

#DIV/0 error - This error happens if you try to divide a number by 0 (zero) or a value that equates to zero which is not possible mathematically.

#VALUE error - The #VALUE error occurs when a formula has a value that is of the wrong data type. Such as text where a number is expected or when dates are evaluated as text.

#REF error - The #REF error happens when a cell reference is invalid. This can happen if a cell is deleted that is referenced by a formula.

#NAME error - The #NAME error happens if you misspelled a function or a named range.

#NUM error - The #NUM error shows up when you try to use invalid numeric values in formulas, like square root of a negative number.

#N/A error - The #N/A error happens when a value is not available for a formula or found in a given cell range, for example in the VLOOKUP or MATCH functions.

#GETTING_DATA error - The #GETTING_DATA error shows while external sources are loading, this can indicate a delay in fetching the data or that the external source is unavailable right now.

7.2 The formula returns an unexpected value

To understand why a formula returns an unexpected value we need to examine the calculations steps in detail. Luckily, Excel has a tool that is really handy in these situations. Here is how to troubleshoot a formula:

1. Select the cell containing the formula you want to examine in detail.
2. Go to tab “Formulas” on the ribbon.
3. Press with left mouse button on "Evaluate Formula" button. A dialog box appears.
   The formula appears in a white field inside the dialog box. Underlined expressions are calculations being processed in the next step. The italicized expression is the most recent result. The buttons at the bottom of the dialog box allows you to evaluate the formula in smaller calculations which you control.
4. Press with left mouse button on the "Evaluate" button located at the bottom of the dialog box to process the underlined expression.
5. Repeat pressing the "Evaluate" button until you have seen all calculations step by step. This allows you to examine the formula in greater detail and hopefully find the culprit.
6. Press "Close" button to dismiss the dialog box.

There is also another way to debug formulas using the function key F9. F9 is especially useful if you have a feeling that a specific part of the formula is the issue, this makes it faster than the "Evaluate Formula" tool since you don't need to go through all calculations to find the issue.

1. Enter Edit mode: Double-press with left mouse button on the cell or press F2 to enter Edit mode for the formula.
2. Select part of the formula: Highlight the specific part of the formula you want to evaluate. You can select and evaluate any part of the formula that could work as a standalone formula.
3. Press F9: This will calculate and display the result of just that selected portion.
4. Evaluate step-by-step: You can select and evaluate different parts of the formula to see intermediate results.
5. Check for errors: This allows you to pinpoint which part of a complex formula may be causing an error.

The image above shows cell reference C16 converted to hard-coded value using the F9 key. The BINOM.INV function requires numerical values which is not the case in this example. We have found what is wrong with the formula.

Tips!

• View actual values: Selecting a cell reference and pressing F9 will show the actual values in those cells.
• Exit safely: Press Esc to exit Edit mode without changing the formula. Don't press Enter, as that would replace the formula part with the calculated value.
• Full recalculation: Pressing F9 outside of Edit mode will recalculate all formulas in the workbook.

Remember to be careful not to accidentally overwrite parts of your formula when using F9. Always exit with Esc rather than Enter to preserve the original formula. However, if you make a mistake overwriting the formula it is not the end of the world. You can “undo” the action by pressing keyboard shortcut keys CTRL + z or pressing the “Undo” button

7.3 Other errors

Floating-point arithmetic may give inaccurate results in Excel - Article

Floating-point errors are usually very small, often beyond the 15th decimal place, and in most cases don't affect calculations significantly.

Functions in 'Statistical' category

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

Excel function categories

Excel categories

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