A-level · Statistical distributions

Approximating a binomial with a normalExam-style questions

When n is large and p not too extreme, approximating B(n, p) by N(np, np(1−p)) — and applying the continuity correction (±0.5) when moving from the discrete binomial to the continuous normal.

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16 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 3 Level 4 Level 5

1
$X \sim B(100, 0.5)$ . Use a normal approximation to estimate $P(X > 55)$ , to 3 d.p.
Level 3 · 4 marksTry it
2
$X \sim B(80, 0.4)$ . State the normal distribution that approximates $X$ .
Level 3 · 2 marksTry it
3
$X \sim B(100, 0.5)$ . Use a normal approximation to estimate $P(X < 45)$ , to 3 d.p.
Level 3 · 4 marksTry it
4
$X \sim B(50, 0.5)$ . Use a normal approximation to estimate $P(X = 25)$ , to 3 d.p.
Level 3 · 4 marksTry it
5
$X \sim B(200, 0.3)$ . Use a normal approximation to estimate $P(X \ge 70)$ , to 3 d.p.
Level 3 · 4 marksTry it

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