CRITBINOM Function

Basic Description

The Excel CRITBINOM function returns the inverse of the Cumulative Binomial Distribution. I.e. for a specific number of independent trials, the function returns the smallest value (number of successes) for which the cumulative binomial distribution is greater than or equal to a criterion value. For example, the Critbinom function could be used to find the smallest number of tosses of a coin for which there is a 50% chance of at least 20 heads.

Syntax: CRITBINOM( trials, probability_s, alpha )

where the arguments are :

trials
The number of independent trials that are to be done

(If this value is a decimal, it is truncated to an integer by Excel)

probability_s The probability of success in one trial
alpha The criterion value of the Cumulative Binomial Distribution (must be between 0 and 1)

 

Binomial Cumulative Distribution Function Chart

Cumulative Distribution Function for the Toss of a Coin in 100 Trials

 

Critbinom Function Example

The chart on the right shows the Cumulative Binomial Distribution Function for 100 tosses of a coin. This curve represents the probability that at most x heads will be thrown from the 100 tosses. The Excel Critbinom function calculates the inverse of the curve on the right. I.e. the Critbinom function calculates the minimum value of x for which the Cumulative Binomial Distribution function is a specified value. This is shown in the spreadsheets below, for three different criterion values.

 Formulas:

Examples of use of the Excel Critbinom Function

 Results:

Excel Critbinom Function Results

 

Critbinom Function Common Errors

If you get an error from the Excel Critbinom Function, this is likely to be one of the following:

#NUM! Occurs if either the supplied trials argument is < 0 or the supplied probability_s argument is < 0 or > 1 or the supplied alpha argument is < 0 or > 1
#VALUE! Occurs if any of the supplied arguments are nonnumeric

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