Lesson 2.04b

2.04b The binomial distribution as a model Quiz: OCR Maths, Unit 14

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 2.04b, The binomial distribution as a model: 20 multiple choice questions for the OCR Maths (H240), Unit 14: Statistical Distributions, written with Revision Ninja.

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The 20 questions

  1. What does the parameter n represent in a binomial distribution model B(n, p)?

    • Number of trials
    • Number of successes
    • Expected variance
    • Probability of success

  2. What does the parameter p represent in the binomial distribution B(n, p)?

    • Probability of failure
    • Number of successes
    • Probability of success
    • Number of trials

  3. Which condition must be met by individual trials in a binomial distribution?

    • Continuous outcomes
    • Independent trials
    • Increasing probabilities
    • Dependent trials

  4. How many possible outcomes must each trial have in a binomial distribution?

    • Exactly three
    • At least two
    • Exactly two
    • Infinitely many

  5. What is the formula for the mean of a binomial distribution B(n, p)?

    • npq^2
    • np(1 - p)
    • np
    • n(1 - p)

  6. What is the formula for the variance of a binomial distribution B(n, p)?

    • n(1 - p)
    • np(1 - p)
    • p(1 - p)
    • np

  7. In binomial distribution notation, how is the probability of failure q defined?

    • 1 / p
    • p - 1
    • 1 - p
    • 1 + p

  8. What type of random variable is modelled by a binomial distribution?

    • Discrete
    • Ordinal
    • Qualitative
    • Continuous

  9. A fair coin is tossed 10 times. What is the binomial model for heads?

    • B(10, 2)
    • B(0.5, 10)
    • B(10, 0.5)
    • B(5, 0.5)

  10. If X ~ B(3, 0.2), what is the value of P(X = 0)?

    • 0.096
    • 0.008
    • 0.384
    • 0.512

  11. If X ~ B(3, 0.2), what is the exact probability P(X = 3)?

    • 0.512
    • 0.096
    • 0.008
    • 0.600

  12. If X ~ B(50, 0.2), what is the mean of X?

    • 2.5
    • 40
    • 10
    • 8

  13. If X ~ B(100, 0.3), what is the variance of X?

    • 30
    • 9
    • 70
    • 21

  14. Which scenario is best modelled by a binomial distribution?

    • Lifespan of 20 lightbulbs
    • Heights of 20 students
    • Speed of 20 passing cars
    • Rolling sixes in 20 rolls

  15. Why does sampling without replacement from a small population violate binomial assumptions?

    • Probability changes
    • Outcomes exceed two
    • Variable becomes continuous
    • Trials are independent

  16. If X ~ B(100, 0.36), what is the standard deviation of X?

    • 36
    • 23.04
    • 4.8
    • 6

  17. If X ~ B(4, 0.5), what is the probability P(X >= 1)?

    • 0.9375
    • 0.8750
    • 0.5000
    • 0.0625

  18. For a fixed number of trials n, which value of p maximises variance?

    • 0.1
    • 0.5
    • 0.9
    • 1.0

  19. In the binomial formula, what does the combination term nCr calculate?

    • Probability of each trial
    • Ways to choose successes
    • Expected mean value
    • Total number of trials

  20. If X ~ B(n, p) is approximated by a normal model, what represents the variance parameter?

    • np^2
    • sqrt(np)
    • np(1 - p)
    • np

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