Lesson N3

N3 Choosing a probability distribution Quiz: AQA Maths, Unit 11

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson N3, Choosing a probability distribution: 20 multiple choice questions for the AQA Maths (7357), Unit 11: Statistics, written with Revision Ninja.

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The 20 questions

  1. Which model is most suitable for the number of successes in a fixed number of independent trials with the same probability of success?

    • Normal
    • Binomial
    • Continuous uniform
    • Exponential

  2. Which distribution best models a continuous, roughly symmetric measurement like height?

    • Continuous uniform
    • Discrete uniform
    • Normal
    • Binomial

  3. Which condition breaks the assumptions required for a binomial distribution model?

    • Fixed trial number
    • Dependent trials
    • Constant probability
    • Two outcomes

  4. Why might a Normal distribution be unsuitable for a continuous variable?

    • Large sample size
    • Bell-shaped frequency
    • Symmetric spread
    • Strong skewness

  5. Which distribution best models the number of heads in 50 fair coin tosses?

    • Uniform(1, 50)
    • Normal(50, 0.5)
    • B(50, 0.2)
    • B(50, 0.5)

  6. Which histogram shape suggests a Normal distribution is an appropriate model?

    • Uniform flat shape
    • Symmetric bell shape
    • Strongly right-skewed
    • Bimodal peak shape

  7. A survey asks 200 random people a yes or no question. Which distribution models the total 'yes' count?

    • Binomial
    • Normal
    • Discrete uniform
    • Continuous uniform

  8. Which conditions permit approximating a Binomial distribution with a Normal distribution?

    • Small n, moderate p
    • Large n, extreme p
    • Small n, extreme p
    • Large n, moderate p

  9. Which model describes the outcome when rolling a single fair six-sided die?

    • Continuous uniform
    • Normal
    • Discrete uniform
    • Binomial

  10. A batch of 50 items has a 3% defect rate. Which distribution models the number of defective items?

    • Uniform(0, 50)
    • B(50, 0.03)
    • B(50, 0.3)
    • Normal(50, 0.03)

  11. Why does a Binomial distribution B(n, p) look bell-shaped when n is large and p = 0.5?

    • Skewness near zero
    • Constant probability density
    • Symmetry around np
    • Equal bin heights

  12. What issue arises when fitting a Normal model to exam marks capped at 100?

    • Data piles at cap
    • Mean exceeds maximum
    • Negative values occur
    • Variance becomes zero

  13. What is a key limitation when using a Normal distribution for real-world tail probabilities?

    • Requires discrete inputs
    • Predicts negative variance
    • Understates extreme values
    • Overstates mean values

  14. Which condition must be satisfied to choose a Binomial model rather than a Normal model?

    • Fixed trial count
    • Continuous data type
    • Variable success probability
    • Unlimited outcomes

  15. Which scenario is best modelled by a Binomial distribution?

    • Score on die
    • Left-handers in sample
    • Test completion time
    • Height of students

  16. Why might assuming p = 0.5 for students guessing true-false questions be invalid?

    • Non-constant probability
    • Two available options
    • Fixed trial number
    • Independent responses

  17. What rule allows $X \sim \text{B}(40, 0.45)$ to be approximated by a Normal distribution?

    • $np$ and $n(1-p) > 5$
    • $n > 30$ only
    • $np < 5$
    • $p = 0.5$ only

  18. Why is a Normal distribution unsuitable for data taking values 0, 1, 2, 3 with mostly 0s?

    • Data is skewed
    • Mean equals variance
    • Data is continuous
    • Data is symmetric

  19. Fifteen shoppers independently buy a product with equal probability. Which distribution models the number of buyers?

    • Binomial
    • Normal
    • Poisson
    • Uniform

  20. A test passes items with probability $p$, but $p$ varies between batches. Which binomial assumption is violated?

    • Fixed trial count
    • Independent trials
    • Two possible outcomes
    • Constant probability

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