Binomial Distribution – AP Statistics | ShowMeClass

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Binomial Distribution

AP Statistics · Unit 5: Probability & Random Variables

Learning Objectives

Identify binomial settings (BINS criteria)

Calculate P(X = k) using the binomial formula

Find cumulative probabilities P(X ≤ k)

Compute mean μ = np and SD σ = √(np(1−p))

Binomial Formula

BINS Criteria

Binary outcomes (success/failure)

Independent trials

Number of trials fixed (n)

Same probability p each trial

BinomialProbabilityAP StatsUnit 5

VIEW:

Trials n 20

Prob. p 0.40

Highlight k 8

P(X ) = —

Mean μ = np—

Variance σ²—

Std Dev σ—

P(X = k)—

P(X ≤ k)—

Sim runs 200

📝 Quick Quiz▼

1. For B(n=10, p=0.3), the mean μ equals:

0.3 3 7 30

2. The standard deviation of B(n=16, p=0.5) is:

4 8 2 16

3. A fair coin is flipped 5 times. P(exactly 3 heads) = ?

0.125 0.3125 0.25 0.5