A-level · Statistical distributions

The binomial distribution as a modelExam-style questions

When the count of "successes" in a fixed number of repeated trials follows a binomial distribution X ~ B(n, p): the four conditions (a fixed number of trials, two outcomes per trial, a constant probability of success, and independent trials), how to identify n and p from a context, how to state a condition for a binomial model, and when the binomial is NOT appropriate.

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

DifficultyAll Level 2 Level 3 Level 4

1
A fair die is rolled $10$ times. $X$ is the number of sixes.
(a) State the distribution of $X$ .
(b) Find $P(X = 2)$ , to 4 d.p.
Level 2 · 3 marksTry it
2
State the four conditions that must hold for a variable to follow a binomial distribution.
Level 2 · 2 marksTry it
3
Twenty seeds are planted; each germinates independently with probability $0.8$ . Suggest a suitable model for the number that germinate, and find the probability that all $20$ germinate, to 4 d.p.
Level 3 · 3 marksTry it
4
Five cards are drawn without replacement from a standard pack, and $X$ is the number of hearts. Explain why $X$ does not follow a binomial distribution.
Level 3 · 1 markTry it
5
A multiple-choice test has $15$ questions, each with $4$ options. A student guesses every answer. Let $X$ be the number correct.
(a) State the distribution of $X$ .
(b) Find $P(X = 5)$ , to 4 d.p.
Level 3 · 3 marksTry it

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