Continuous Distributions

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Edexcel IAL Statistics 2 (WST02)

Continuous Distributions

The big idea: Two continuous models matter here: the rectangular (uniform) distribution, and the normal distribution as an approximation to discrete ones.

Summary — What This Chapter Covers

X ~ U[a, b]: f(x) = 1/(b − a), mean (a + b)/2, variance (b − a)²/12.
B(n, p) ≈ N(np, np(1 − p)) when n is large and p is close to ½.
Po(λ) ≈ N(λ, λ) when λ is large (λ > 10).
Always apply a continuity correction.

1. The Continuous Uniform Distribution

Uniform

Constant density

Probabilities are lengths of intervals divided by (b − a).

2. Normal Approximations to the Binomial and Poisson

Normal approximation

Continuity corrections

A discrete value r becomes the interval r − 0.5 to r + 0.5.

Worked Example

X ~ B(100, 0.4). Use a normal approximation to find P(X ≤ 45).

Memorise

Uniform

(a + b)/2, (b − a)²/12

B → N

N(np, npq)

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Continuous Distributions