AP®︎ Statistics: Topic 2.10 Flashcards

Master key terms and definitions for Topic 2.10 of AP Statistics – The Binomial Distribution to help you prep for quizzes and the AP exam.

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Term

Binomial Random Variable

Definition

A discrete random variable that counts the number of successes in a fixed number n of independent trials with binary outcomes and the same success probability p

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Binomial Random Variable
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A discrete random variable that counts the number of successes in a fixed number n of independent trials with binary outcomes and the same success probability p

2.10.A2.10.A.1
X ~ Bin(n, p)
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Notation that X has a binomial distribution with n trials and probability of success p on each trial

2.10.A2.10.A.1
BINS
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Binary outcomes, Independent trials, fixed Number of trials, Same probability of success on each trial

2.10.A2.10.A.1
Success
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The outcome being counted in a binomial setting; it need not be desirable

2.10.A2.10.A.1
Binomial Probability Function
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P(X = x) = (n choose x)p^x(1 − p)^(n − x), for x = 0, 1, ..., n; gives the probability of exactly x successes

2.10.E2.10.E.1
n Choose x
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Binomial coefficient, written (n choose x) = n!/[x!(n − x)!], counting the number of ways x successes can be arranged among n trials

2.10.E2.10.E.1
Complement Rule for Binomial Probabilities
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Use the opposite event, often for upper tails; for example, P(X ≥ k) = 1 − P(X ≤ k − 1)

2.10.E2.10.E.1
binompdf(n, p, x)
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Calculator function that gives P(X = x) for a binomial random variable

2.10.E2.10.E.1
binomcdf(n, p, x)
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Calculator function that gives P(X ≤ x) for a binomial random variable

2.10.E2.10.E.1
Mean of a Binomial Distribution
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μX = np

2.10.B2.10.B.1
Variance of a Binomial Distribution
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σX² = np(1 − p)

2.10.B2.10.B.1
Standard Deviation of a Binomial Distribution
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σX = √(np(1 − p))

2.10.B2.10.B.1
Binomial Simulation
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Model n independent trials with success probability p, count successes for one repetition, repeat many times, and use relative frequency to estimate the probability

2.10.D2.10.D.1
Possible Values of X for a Binomial Distribution
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0, 1, 2, ..., n

2.10.A2.10.A.1
Parameters of Bin(n, p)
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n = fixed number of trials; p = probability of success on each trial

2.10.A2.10.A.1
At Most k
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P(X ≤ k)

2.10.E2.10.E.1
Fewer Than k
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P(X < k) = P(X ≤ k − 1)

2.10.E2.10.E.1
At Least k
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P(X ≥ k)

2.10.E2.10.E.1
More Than k
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P(X > k) = P(X ≥ k + 1)

2.10.E2.10.E.1
Between a and b, Inclusive
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P(a ≤ X ≤ b) = P(X ≤ b) − P(X ≤ a − 1)

2.10.E2.10.E.1