A-level · Statistical distributions

Cumulative binomial probabilitiesExam-style questions

Finding P(X ≤ r), P(X < r), P(X ≥ r), P(X > r) and P(a ≤ X ≤ b) for a binomial distribution by building everything from the cumulative function P(X ≤ r) (binomcdf), with care over the off-by-one when an inequality is strict or "at least". Includes the complement for "≥" and "two-stage" problems where the success of one binomial becomes the trial of another.

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

DifficultyAll Level 3 Level 4 Level 5

1
$X \sim B(20, 0.3)$ . Find $P(X \le 5)$ , to 4 d.p.
Level 3 · 2 marksTry it
2
$X \sim B(15, 0.2)$ . Find $P(X \ge 4)$ , to 4 d.p.
Level 3 · 2 marksTry it
3
$X \sim B(25, 0.4)$ . Find $P(X < 10)$ , to 4 d.p.
Level 3 · 2 marksTry it
4
$X \sim B(30, 0.5)$ . Find $P(12 \le X \le 18)$ , to 4 d.p.
Level 3 · 2 marksTry it
5
$X \sim B(20, 0.25)$ . Find $P(X > 7)$ , to 4 d.p.
Level 3 · 2 marksTry it

6 more questions on cumulative binomial probabilities

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