Binomial Distribution (AQA A-Level Mathematics): Quizzes

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The Binomial Distribution
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How many outcomes does a binomial distribution describe?

Two outcomes

In the notation X∼B(n,p)X \sim B(n, p), what does nn represent?

Number of trials

In X∼B(n,p)X \sim B(n, p), what does pp represent?

Probability of success each time

In X∼B(n,p)X \sim B(n, p), what does XX refer to?

Number of wins obtained

Which two conditions must hold for a binomial distribution?

Independent trials, fixed probability

If X∼B(n,p)X \sim B(n, p), what is the mean of XX?

npnp

If X∼B(n,p)X \sim B(n, p), what is the variance of XX?

np(1−p)np(1-p)

What is the formula for P(X=x)P(X = x) when X∼B(n,p)X \sim B(n, p)?

(nx)px(1−p)n−x\binom{n}{x} p^x (1-p)^{n-x}

How is P(X≤1)P(X \leq 1) calculated?

P(X=0)+P(X=1)P(X = 0) + P(X = 1)

Which situation is suitable for binomial distribution?

Fixed trials, binary outcome, constant pp

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