How to use the BINOM.DIST function

What is the BINOM.DIST function?

The BINOM.DIST function calculates the individual term binomial distribution probability, use this function when

• the success probability is constant through all trials
• you know the number of trials
• the outcome is either a success or failure
• each trial is independent of the other trials.

The BINOM.DIST function was introduced in Excel 2010 and replaces the outdated BINOMDIST function.

1. Introduction

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 the individual term binomial distribution probability?

The individual term binomial distribution probability is the probability of exactly k successes in n trials with a given success probability p, calculated using combinations to determine the number of ways k successes can occur in those trials.

What are combinations?

A combination is a way of selecting items from a collection where the order of selection does not matter.

For example, if you have three fruits, say an apple, an orange, and a pear. There are three combinations of two that can be drawn from this set:

• apple and a pear
• apple and an orange
• pear and an orange

2. Syntax

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

3. Arguments

number_s	Required. The number of successful tests.
trials	Required. How many independent tests.
probability_s	Required. The probability of success in each test.
cumulative	Required. A boolean value. TRUE - cumulative distribution function. FALSE - probability mass function.

What is cumulative binomial distribution?

The cumulative binomial distribution function gives the probability that a binomial random variable with a given number of trials and success probability will take on a value less than or equal to a specified number of successes x.

What is probability mass function?

A probability mass function is a function that defines a discrete probability distribution by providing the probability that each of a countable number of possible discrete outcomes will occur for a random variable.

What is a binomial random variable?

A binomial random variable is a discrete random variable that represents the number of "successes" in a fixed number of independent binary trials, where each trial has the same probability of success.

What are discrete probabilities?

Discrete probabilities are individual separated probabilities assigned to each of a countable number of possible outcomes that sum to 1, like rolling a die where each number has its own exact probability, as opposed to continuous distributions.

4. Example 1

The probability that a customer accepts an offer is estimated to be 60%. The offer is given to 20 customers. What is the probability that at most 12 of them accepts the offer?

To solve this we need to use the binomial distribution. It models the number of successes in a fixed number of independent trials (20 customers). Each trial has the same probability of success (0.6 or 60%).

Let x be the random variable representing the number of customers who accepts the offer. Then x follows a binomial distribution with parameters n = 20 (number of trials) and p = 0.6 (probability of success).

The probability we want to find is P(x ≤ 12) which is the cumulative probability of the binomial distribution from 0 up to 12.

Formula in cell C21:

The formula returns approx. 0.5841, in other words, the probability is 58.4% that up to 12 customers accepts the offer.

The chart in the image above shows an orange line representing the cumulative probability. Go to 12 on the x-axis and find where the orange line intersects the middle of the column. The secondary y-axis to the right shows a value just below 0.6 which seems to match the calculated number 0.5841

5. Example 2

There are 22 machines that operate independently of each other in a factory. The probability of a breakdown occurring during a day is 0.1 for each of the machines. What is the probability that three machines will stop during a certain day?

The binomial distribution is what we need in this example. It models the number of successes (machine breakdowns) in a fixed number of independent trials (22 machines), where each trial has the same probability of success (0.1 or 10%).

Let x be the random variable representing the number of machines that break down during the day. Then x follows a binomial distribution with parameters n = 22 (number of machines) and p = 0.1 (probability of breakdown for each machine).

The probability we want to find is P(X = 3), which is the probability mass function of the binomial distribution evaluated at 3.

The formula returns 0.208, in other words, the probability is 20.8% that exactly 3 machines break down during a day.

The chart in the image above shows blue chart columns representing the probability mass function of the binomial distribution. Go to 3 on the x-axis and find the value value for that column. The y-axis to the left shows a value just above 0.2 which seems to match the calculated number 0.208

6. Example 3

There are 30 students in a class. There is a 50% risk that each student, independently of each other, will catch a harmless but highly contagious cold. What is the chance that 12 students or less will attend school on the same day?

We need to find the probability that 12 or fewer students will not catch the cold, which is the same as the probability that 18 or more students will catch the cold.

• Total number of students: 30
• Probability of catching the cold for each student: 0.5 (or 50%)

We want to find P(X ≥ 18), which is the probability that 18 or more students will catch the cold.

P(X ≥ 18) = 1 - P(X ≤ 17)

We can calculate P(X ≤ 17) using the cumulative distribution function of the binomial distribution and then take the complement to find P(X ≥ 18).

Formula in cell C21:

The formula in cell C21 returns 0.181 which is 18.1%. This means that there is a 18.1% chance that 12 students or less will attend school on the same day.

7. Function not working

The BINOM.DIST function returns

• #VALUE! error value if number_s, trials or probability_s argument is non-numeric.
• #NUM! error value if:
  • number_s <= 0 (zero)
  • number_s > trials
  • probability_s < 0 (zero)
  • probability_s > 1
  • A = B

number_s and trials are converted into integers.

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 C3 converted to hard-coded value using the F9 key. The BINOM.DIST 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.

'BINOM.DIST' function examples

The following article has a formula that contains the BINOM.DIST function.

Functions in 'Statistical' category

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

Excel function categories

Excel categories

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