Binomial Distributions

Binomial Probability Distributions

In this section, we examine Binomial Probability Distributions:

• They are discrete distributions
• They measure the probability of a certain number, [latex]x[/latex], of successes occurring
• We need both the number of trials ([latex]n[/latex]), and the probability of success ([latex]p[/latex]) to define a binomial distribution

The sections are organized as follows:

1. An introduction, properties of Binomial Distributions and how to calculate the probability of exactly [latex]x[/latex] successes using the formula.
2. How to calculate the probability of exactly [latex]x[/latex] successes using the Excel’s =BINOM.DIST function.
3. How to calculate the probability of at most [latex]x[/latex] number of successes.
4. How to calculate the probability of more than [latex]x[/latex] number of successes.
5. How to calculate the probability of at least [latex]x[/latex] successes or, [latex]P(X \ge x)[/latex].
6. How to calculate the mean and standard deviation of binomial distributions.