Choosing Distributions (A Level only) (AQA A-Level Mathematics): Flashcards

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Modelling with Distributions
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Binomial distribution models

Number of successes in fixed independent trials

Binomial condition: trial outcomes

Two possible outcomes (success or failure)

Binomial condition: trials

Independent

Binomial condition: probability of success

Remains constant

Binomial formula P(X=k)P(X=k)

(nk)pk(1−p)n−k\binom{n}{k} p^k (1-p)^{n-k}

Normal distribution symmetry

Symmetric around the mean

Normal dist: mean, median, mode

All equal

Empirical rule: % within 1 std dev of mean

68%

Empirical rule: % within 2 std devs of mean

95%

Z-score formula

Z=X−μσZ = \frac{X - \mu}{\sigma}

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Probability Distributions

Binomial Distribution

Normal Distribution (A Level only)

Choosing Distributions (A Level only)

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Probability Distributions

Binomial Distribution

Normal Distribution (A Level only)

Choosing Distributions (A Level only)

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Probability Distributions

Binomial Distribution

Normal Distribution (A Level only)

Choosing Distributions (A Level only)

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Probability Distributions

Binomial Distribution

Normal Distribution (A Level only)

Choosing Distributions (A Level only)

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