Binomial Distribution and Probabilities

These flashcards cover key concepts, definitions, and examples related to binomial distributions and probabilities.

Binomial Distribution

A statistical distribution that describes the number of successes in a fixed number of independent trials, each with the same probability of success.

Mean (μ) for Binomial Distribution

Calculated as μ = np, where n is the number of trials and p is the probability of success.

Standard Deviation (σ) for Binomial Distribution

Calculated as σ = √(npq), where q = 1 - p is the probability of failure.

Probability of Success (p)

The likelihood of achieving a success in a single trial of a binomial experiment.

Probability of Failure (q)

Calculated as q = 1 - p, representing the likelihood of failure in a single trial.

Binomial Probability Function

A function that gives the probability of achieving exactly x successes in n trials, defined as P(X = x) = (n choose x) p^x q^(n-x).

Conditions for Binomial Setting

A binomial setting requires two possible outcomes, independent trials, a fixed number of trials, and consistent probability of success across trials.

10% Rule (10% Condition)

If trials are not independent, it is acceptable to proceed as binomial if the sample size is less than 10% of the population.

Combination (n choose k)

The number of ways to choose k successes from n trials, represented mathematically as n!/(k!(n-k)!).

Example of Binomial Scenario

If a company produces 500 chips with a 2% defect rate, the variable representing the number of defective chips is a binomial random variable.