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Binomial Probability Distribution Function (BinomPDF) and Binomial Cumulative Distribution Function (BinomCDF) are two types of probability distribution functions commonly used in statistics to model the likelihood of a certain event occurring.
The Binomial Probability Distribution Function (BinomPDF) calculates the probability of obtaining a specific number of successes in a fixed number of independent trials, given a certain probability of success for each trial. It is represented by the formula P(x;n,p) = (nCx) * p^x * (1-p)^(n-x), where x is the number of successes, n is the number of trials, and p is the probability of success.
On the other hand, the Binomial Cumulative Distribution Function (BinomCDF) calculates the probability of obtaining a number of successes less than or equal to a specific value in a fixed number of independent trials. It is represented by the formula P(x≤k;n,p) = ∑ from i=0 to k of (nCi) * p^i * (1-p)^(n-i), where k is the desired number of successes.
An example of Binomial Probability Distribution Function would be calculating the probability of getting exactly 2 heads when flipping a fair coin 5 times, given that the probability of getting a head is 0.5. On the other hand, an example of Binomial Cumulative Distribution Function would be calculating the probability of getting 2 or less heads when flipping a fair coin 5 times, given the probability of getting a head is 0.5.
In summary, Binomial Probability Distribution Function and Binomial Cumulative Distribution Function are both useful tools for calculating the likelihood of certain events occurring in a fixed number of independent trials, but they differ in the specific values they calculate and the types of questions they can answer.
BinomPDF vs BinomCDF: The Difference (Plus Examples)
The is one of the most commonly used distributions in all of statistics.
On a TI-84 calculator there are two functions you can use to find probabilities related to the binomial distribution:
- binompdf(n, p, x): Finds the probability that exactly x successes occur during n trials where the probability of success on a given trial is equal to p.
- binomcdf(n, p, x): Finds the probability that x successes or fewer occur during n trials where the probability of success on a given trial is equal to p.
You can access each of these functions on a TI-84 calculator by pressing 2nd and then pressing VARS. This will take you to a DISTR screen where you can then use binompdf() and binomcdf():
The following examples show how to use each of these functions in practice.
Examples: How to Use Binompdf()
The following examples show how to use the binompdf() function.
Example 1: Free-Throw Attempts
Jessica makes 80% of her free-throw attempts. If she shoots 10 free throws, what is the probability that she makes exactly 7?
To answer this, we can type in the following formula:
The probability that she makes exactly 7 is .2013.
Example 2: Fraudulent Transactions
A bank knows that 3% of all transactions are fraudulent. If 20 transactions occur in a given day, what is the probability that exactly 2 are fraudulent?
To answer this, we can type in the following formula:
Examples: How to Use Binomcdf()
The following examples show how to use the binomcdf() function.
Example 1: Free-Throw Attempts
Jessica makes 50% of her free-throw attempts. If she shoots 10 free throws, what is the probability that she makes 7 or less?
To answer this, we can type in the following formula:
The probability that she makes 7 or less free throws is .9453.
Example 2: Fraudulent Transactions
A bank knows that 3% of all transactions are fraudulent. If 20 transactions occur in a given day, what is the probability that more than 2 transactions are fraudulent?
To answer this, we can type in the following formula:
The probability that more than 2 transactions are fraudulent is .021.