Binomial distribution

Definition

The binomial distribution is a probability distribution that summarizes the likelihood of a value taking one of two independent states and is determined by the number of trials and the probability of success in each trial.

5 Must Know Facts For Your Next Test

1. A binomial distribution is characterized by two parameters: $n$ (number of trials) and $p$ (probability of success).
2. The mean of a binomial distribution is given by $np$, where $n$ is the number of trials and $p$ is the probability of success.
3. The standard deviation for a binomial distribution can be calculated using $\sqrt{np(1-p)}$.
4. In hypothesis testing, the binomial distribution can be used to test claims about a population proportion when sample sizes are sufficiently large.
5. For constructing confidence intervals for a population proportion, the normal approximation to the binomial distribution is often used when both $np \geq 5$ and $n(1-p) \geq 5$.

Review Questions

• What are the key parameters that define a binomial distribution?
• How do you calculate the mean and standard deviation of a binomial distribution?
• When can normal approximation be applied to a binomial distribution?

Related terms

Population Proportion:

The fraction or percentage that represents part of a total population with a particular characteristic.

Hypothesis Testing:

A statistical method used to make decisions about population parameters based on sample data.

Normal Approximation:

An approach where the binomial distribution is approximated by the normal distribution under certain conditions, typically when sample size is large.