Lesson 2.03e

2.03e Modelling with probability: Modelling with probability (2.03e) Quiz: OCR Maths, Unit 13

20 questions

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Lesson 2.03e, Modelling with probability: Modelling with probability (2.03e): 20 multiple choice questions for the OCR Maths (H240), Unit 13: Probability, written with Revision Ninja.

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The 20 questions

  1. What key condition must hold for trials in a Binomial distribution?

    • Independence
    • Continuous outcomes
    • Variable probabilities
    • Dependence

  2. In a discrete probability distribution table, what must all probabilities sum to?

    • 0
    • 1
    • 0.5
    • 100

  3. What is the formula for the mean of a Binomial distribution?

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

  4. What is the formula for the variance of a Binomial distribution?

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

  5. For P(X=x) = kx with x in {1, 2, 3}, what is the value of k?

    • 1/6
    • 1/2
    • 1/3
    • 1/4

  6. Which two parameters fully define a Binomial distribution model?

    • n and p
    • mean and variance
    • a and b
    • n and sigma

  7. If trials are assumed independent when positively correlated, what happens to calculated variance?

    • It stays accurate
    • It equals zero
    • It is overestimated
    • It is underestimated

  8. How many possible outcomes must each trial have in a Binomial model?

    • Exactly one
    • Exactly two
    • At least three
    • Any finite number

  9. What is the mean value of a random variable X ~ B(50, 0.2)?

    • 8
    • 40
    • 2.5
    • 10

  10. What is the variance of a Binomial distribution X ~ B(100, 0.3)?

    • 21
    • 9
    • 70
    • 30

  11. Modelling daily weather as independent trials is unrealistic because weather exhibits what feature?

    • Serial dependence
    • Binary outcomes
    • Fixed sample size
    • Constant probability

  12. If P(X=1) = 0.2, P(X=2) = 0.5, and P(X=3) = c, what is c?

    • 0.25
    • 0.1
    • 0.7
    • 0.3

  13. In the distribution notation X ~ B(n, p), what does n represent?

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

  14. What type of random variable takes only a finite set of separate values?

    • Continuous
    • Discrete
    • Normal
    • Uniform continuous

  15. What is the standard deviation formula for a Binomial distribution?

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

  16. Sampling without replacement from a small population violates which assumption of a Binomial model?

    • Two outcomes
    • Discrete values
    • Constant probability
    • Fixed trials

  17. If P(X=x) = 0.1x for x in {1, 2, 3, 4}, what is P(X > 2)?

    • 0.3
    • 0.6
    • 0.4
    • 0.7

  18. If a fair coin is tossed 12 times, what is the value of n?

    • 6
    • 12
    • 0.5
    • 2

  19. What is the standard deviation of the distribution X ~ B(16, 0.5)?

    • 2
    • 8
    • 1
    • 4

  20. Which value cannot be a valid probability in a discrete probability distribution?

    • 0.5
    • 1
    • 0
    • 1.2

All OCR Maths quizzes