Topic 8 of 8 · Form 5
Probability and statistics
Stem-and-leaf, box plots, histograms, cumulative frequency; mean, standard deviation (including coded data: Σ(x − a) and Σ(x − a)²), median and quartiles.
Notes for this topic 1 file, in order
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Representation of data
Stem-and-leaf, box plots, histograms, cumulative frequency; mean, standard deviation (including coded data: Σ(x − a) and Σ(x − a)²), median and quartiles.
Permutations and combinations
Arrangements with repeated items and restrictions; selections.
Probability
Addition and multiplication rules; mutually exclusive and independent events; conditional probability P(A|B) = P(A ∩ B)/P(B).
Discrete random variables
Probability distributions; E(X) = Σxp; Var(X) = Σx²p − [E(X)]²; binomial distribution B(n, p) with mean np and variance np(1 − p); geometric distribution Geo(p) with P(X = r) = (1 − p)^(r − 1)p and mean 1/p.
Worked example: X ~ B(10, 0.3). Find P(X = 3).
¹⁰C₃ × 0.3³ × 0.7⁷ = 120 × 0.027 × 0.08235 = 0.267
The normal distribution
Standardising Z = (X − μ)/σ; finding probabilities and unknown μ or σ; normal approximation to the binomial with continuity correction (when np > 5 and nq > 5).
Worked example: X ~ N(40, 25). Find P(X > 47).
z = 1.4 → 1 − 0.9192 = 0.0808
Check yourself
- Find the mean and variance of B(20, 0.25).
- For Geo(0.2), find P(X = 3).
- X ~ N(100, 15²). Find P(X < 85).
Show answers
- 5 and 3.75
- 0.8² × 0.2 = 0.128
- z = −1 → 0.1587
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