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 model is most suitable for a continuous measurement such as height, with a roughly symmetric spread?

    • A distribution with only zero values
    • Normal
    • Discrete uniform
    • Binomial

  3. When may a binomial model be inappropriate?

    • When the number of trials is fixed
    • When each trial has only two possible outcomes
    • When the trials are not independent
    • When the probability of success is constant

  4. When may a Normal model be inappropriate for a variable?

    • When the variable is the sum of many small independent effects
    • When the histogram is symmetric and bell-shaped
    • When the variable is strongly skewed with a long right tail
    • When the variable measures adult heights

  5. The number of heads in 50 tosses of a fair coin is best modelled by which distribution?

    • Continuous uniform from 0 to 50
    • Binomial with n = 25 and p = 0.5
    • Binomial with n = 50 and p = 0.5
    • Normal with mean 0.5

  6. Which feature of a histogram suggests a Normal model is appropriate for a continuous measurement?

    • A roughly symmetric bell shape
    • Two outcomes only
    • Discrete integer values only
    • A heavily skewed shape with many zeros

  7. A survey of 200 people asks yes or no whether they use public transport, with the proportion unknown. Which model is most appropriate for the count of yes answers?

    • Binomial with n = 100
    • Normal with mean 200
    • Continuous uniform from 0 to 200
    • Binomial with n = 200

  8. A binomial distribution is approximated by a Normal distribution. Which condition typically justifies this?

    • n is 5 and p is 0.001
    • n is small and p is close to 0
    • n is large and p is not too close to 0 or 1
    • p is exactly 0 or 1

  9. A die is rolled once, with each face from 1 to 6 equally likely. Which model describes the score?

    • Continuous uniform from 0 to 6
    • Normal distribution
    • Binomial with n = 6
    • Discrete uniform distribution

  10. A factory checks 50 items from a large run in which 3% are defective. Which model is most appropriate for the number of defective items?

    • Continuous uniform from 0 to 50
    • Binomial with n = 3 and p = 0.5
    • Normal with mean 1.5 and no limits
    • Binomial with n = 50 and p = 0.03

  11. Why does a binomial histogram look bell-shaped for large n with p close to 0.5?

    • The distribution is always skewed to the right
    • The distribution is always flat
    • The distribution has no mean
    • The distribution is approximately symmetric around np

  12. Exam marks are capped at 100 and many candidates score exactly 100. What is the best critique of using a Normal model?

    • A binomial model must be used instead
    • The model fails only if the mean is below 50
    • The cap cuts off the distribution, so a Normal model may fit poorly near 100
    • The model is perfect because marks are continuous

  13. A Normal model is used for adult heights. What is a valid critique of its tail probabilities?

    • The Normal curve is only valid for discrete data
    • Normal tail probabilities are always exactly zero
    • Normal tails are heavier than real data
    • Normal tails decay quickly, so extreme values may be understated in real data

  14. Which is a key check when choosing between a binomial and a Normal model for a count?

    • Whether the mean exceeds 100
    • Whether the histogram has exactly two peaks
    • Whether the variable is measured in metres
    • Whether the situation has a fixed number of trials with two outcomes each

  15. Which situation could be modelled by a binomial distribution?

    • The number of left-handed people in a random sample of 40, assuming independence and a fixed proportion
    • The lifetime of a battery in hours
    • The heights of students in a school
    • The time taken to finish a race measured continuously

  16. A model assumes each student guesses a true-false question with probability 0.5 of being correct. What is a valid critique?

    • The binomial model requires more than two outcomes
    • Guessing always gives exactly 0.5 for every student
    • Students may not guess at random, so the success probability may differ between students
    • True-false questions cannot be modelled at all

  17. X ~ B(40, 0.45). Is a Normal approximation reasonable?

    • No, since p is not 0.5
    • Yes, since np and n(1 - p) are both large
    • Yes, since n is greater than p
    • No, since the binomial is discrete

  18. A variable takes only the values 0, 1, 2 and 3, with most values equal to 0. Which is a sound reason to reject a Normal model?

    • The sample size is above 30
    • The histogram has a single peak
    • The sample mean is 0.4
    • The data are discrete, highly skewed and take few values

  19. Fifteen shoppers each independently buy a product with the same probability. Which model describes the number who buy it?

    • Binomial with n = 1 and p = 15
    • Normal with variance 15
    • Binomial with n = 15
    • Continuous uniform from 0 to 15

  20. A quality test passes each item with probability p, but p changes between batches. Which binomial assumption is broken?

    • A constant probability of success across trials
    • A fixed number of trials
    • Two possible outcomes per trial
    • A finite mean

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