Binomial Probability Distributions with Microsoft Excel

A binomial distribution describes the outcome of a multi-step experiment, consisting of
n same trials, where each trial ends in whether a success or a failure and the probability of
a success p does not convert from trial to trial. This useful statistical determination can be performed relatively precisely using Microsoft Excel using the Excel Binomdist, Critbinom and Negbinomdist functions.

Binomial Probability Distributions with Microsoft Excel

Binomial Probability Distributions with Microsoft Excel

---

Binomial Probability Distributions with Microsoft Excel

Binomial Probability Distributions with Microsoft Excel

Note, however, that when production binomial probability calculations, the trials must also be independent so that success in one trial does not affect the probability of success in someone else trial. The binomial random changeable x is the number of successes observed in n trials.

If samples are not replaced, and therefore the outcome of one trial changes the probability of success in someone else trial, you need to use the hypergeometric probability distribution Excel function.

Using Excel's Binomdist Function

For example, if you flip a coin n times and "heads" is called a success, then the random variable
x would be the number of heads observed in n flips. It could take the values 1,2,3,...,n with different probabilities.

The Binomdist function uses the following syntax:

=Binomdist(x,n,p,cumulative)

If you want to find the probability of exactly x successes, enter False as the fourth (cumulative) argument. If you want to find the probability of x or fewer successes, enter True as the fourth argument.

For example, if you were to flip a fair coin 20 times and wanted to find the probability of it turning up "heads" exactly 10 times, the function looks like this:

=Binomdist(10,20,0.5,False)

The function returns the value 0.176197052. If you wanted to find the probability of getting
10 or fewer heads, you replace the False with True, and the function returns the value 0.588098526.

Using Excel's Critbinom Function

The acceptance criterion function, Critbinom, is used for capability control of a yield process. You use this function to find the maximum number of defective items that a person can find in a lot and still allow acceptance of the lot. Inspectors should accept the lot if they find this number or fewer defective items and reject the lot if they find more defective items.

To determine the acceptance criterion, you need to know the number of items in the lot, the probability of accepting each item, and the producer's allowable risk (alpha) for rejecting an appropriate lot.

The Critbinom function uses the following syntax:

=Critbinom (trials, probability_s, alpha)

where trials is the number of trials, probability's is the probability of a success on each trial,
and alpha is the criterion value. Probability's and alpha are both in the middle of 0 and 1.

Using Excel's Negbinomdist Function

If the number of successes is fixed in a binomial distribution and you want to find the number of trials, use the Negbinomdist function. This function returns the probability that there will be a confident number of failures before the threshold number of successes, given the constant probability of a success.

For example, if you need to find 20 right 2 by 4s from a stack, and you know the probability that a board in the stack is right is 0.2 (20%), you can use the Negbinomdist to find that there is about a 2% probability that you will reject 75 boards before seeing all 20 right ones.

The Negbinomdist function uses the following syntax:

=Negbinomdist (number failures, number successes, probability of success)

For this example, the function looks like this:

=negbinomdist (75, 20, 0.2)

Binomial Probability Distributions with Microsoft Excel

Horizontal Storage Shed Izunami Ionic Ceramic Flat Iron Night Owl Battery Backup Sump Pump system