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
$40\%$ of items from a production line are type A. In a sample of $150$ , let $X$ be the number of type A.
(a) State a suitable normal approximation for $X$ .
(b) Estimate $P(X > 65)$ , to 3 d.p.
Level 5 · 5 marksTry it
2
$10\%$ of items from a production line are faulty. A batch of $900$ items is inspected.

Use a normal approximation to estimate the probability that at most $75$ items are faulty, giving your answer to 3 significant figures. (5 marks)
Level 5 · 5 marksTry it