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  2. AP Statistics
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What is the formula for calculating binomial probability P(X = x)?

P(X=x)=(nx)∗px∗(1−p)(n−x)P(X = x) = \binom{n}{x} * p^x * (1-p)^{(n-x)}P(X=x)=(xn​)∗px∗(1−p)(n−x)

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What is the formula for calculating binomial probability P(X = x)?

P(X=x)=(nx)∗px∗(1−p)(n−x)P(X = x) = \binom{n}{x} * p^x * (1-p)^{(n-x)}P(X=x)=(xn​)∗px∗(1−p)(n−x)

What does 'n' represent in the binomial probability formula?

n = number of trials

What does 'p' represent in the binomial probability formula?

p = probability of success on a single trial

What does 'x' represent in the binomial probability formula?

x = number of successes

What is the formula for the standard deviation of a binomial distribution?

np(1−p)\sqrt{np(1-p)}np(1−p)​

What are the differences between binomPDF and binomCDF?

binomPDF: Probability of exactly x successes | binomCDF: Probability of x or fewer successes

What are the differences between theoretical and empirical probability?

Theoretical: Uses rules of probability | Empirical: Uses observed frequencies from simulations

What are the differences between binomial and geometric distributions?

Binomial: Fixed number of trials | Geometric: Number of trials until the first success

What are the differences between success and failure in a binomial trial?

Success: The outcome of interest | Failure: Any outcome that is not the outcome of interest

What are the differences between independent and dependent trials?

Independent: Outcome of one trial doesn't affect others | Dependent: Outcome of one trial affects others

Explain the concept of independent trials in a binomial setting.

The outcome of one trial does not influence the outcome of any other trial.

Explain the purpose of binomPDF.

binomPDF calculates the probability of exactly x successes in n trials.

Explain the purpose of binomCDF.

binomCDF calculates the probability of x or fewer successes in n trials.

What are the conditions (BINS) for a binomial setting?

Binary (Success/Failure), Independent, Number of trials is fixed, Same probability of success.

Why is it important to interpret binomial probabilities in context?

Interpreting in context provides meaning to the numerical result and is often required for full credit on assessments.