C

Binomial Probability Distributions

Binomial Probability Distributions: Conditions

  • A procedure generates a binomial probability distribution if four conditions are met:

    1. Two Outcomes: Each trial has exactly two outcomes: Success and Failure. Define Success beforehand.

    2. **Fixed Number of Trials (n): **The number of trials must be known and fixed.

    3. Independent Trials: Trials must be independent of each other (e.g., with replacement).

    4. **Constant Probability of Success (p): **The probability of success must remain the same for each trial.

Components of a Binomial Procedure

  • Success: The specific outcome of interest (an action, not a quantity).

  • n: The total number of trials.

  • x: The specific number of successes desired (must be a whole number).

  • p: The probability of success in a single trial (0 \leq p \leq 1).

  • q: The probability of failure in a single trial, calculated as q = 1 - p .