C

binomial distributions

Binomial Probability Basics

  • Binomial Situation: Involves two outcomes (success/failure), given parameters such as number of trials (n) and probability of success (p).

  • Examples Used: Auditing (1% probability), patient side effects (76% probability).

Key Formulas

  • Mean: (\mu = n \times p)

  • Variance: (\sigma^2 = n \times p \times q) where (q = 1 - p)

  • Standard Deviation: (\sigma = \sqrt{\sigma^2})

Probability Calculations

  • Use binomial probability functions (BINOM.PDF) to compute probability of exact successes.

    • Format: BINOM.PDF(n, p, x) where:

    • n = number of trials

    • p = probability of success

    • x = number of successes

  • Calculating probabilities for more than one success involves summing individual probabilities:

    • Example: At least 10 means calculate for x=10, x=11, x=12 and sum values.

Example Scenarios

  • Total Trials: Always identify n (total number of possible outcomes).

  • Success: Clarify what constitutes a success (e.g., being audited, experiencing side effects).

Important Probability Concepts

  • Small Probability: If probability < 0.05, event considered unusual.

  • Probability Setup: Always structure your answers by demonstrating setups to show understanding, essential for tests.

Common Errors to Avoid

  • Misidentifying p or not clarifying what success means based on given scenario.

  • Confusing values provided in questions (e.g., using total seats instead of booked passengers in flight examples).

  • Forgetting that normals for probabilities (range between 0 and 1).

Numerical Outputs

  • Calculation must provide rounded outputs (typically to 2-4 decimal places depending on instructions).