Lesson 2.04e

2.04e Using the normal distribution Quiz: OCR Maths, Unit 14

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 2.04e, Using the normal distribution: 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. In the normal distribution notation X ~ N(mu, sigma^2), what does sigma^2 represent?

    • Mean
    • Median
    • Standard deviation
    • Variance

  2. What percentage of values lie within one standard deviation of the mean in a normal distribution?

    • About 68%
    • About 99.7%
    • About 50%
    • About 95%

  3. What percentage of values lie within two standard deviations of the mean in a normal distribution?

    • About 68%
    • About 95%
    • About 80%
    • About 99.7%

  4. Where do the points of inflection occur on a normal distribution curve?

    • x = mu ± sigma
    • x = mu ± 2sigma
    • x = mu ± 3sigma
    • x = mu

  5. What is the mean of the standard normal distribution Z?

    • 0
    • 1
    • sigma
    • 0.5

  6. What is the variance of the standard normal distribution Z?

    • 0
    • 1
    • 0.5
    • sigma

  7. Which formula transforms a normal variable X into the standard normal variable Z?

    • Z = (X - sigma) / mu
    • Z = (mu - X) / sigma
    • Z = (X - mu) / sigma^2
    • Z = (X - mu) / sigma

  8. What is the total area under a normal distribution probability density curve?

    • 2
    • 1
    • 100
    • 0.5

  9. If a normal variable X is defined as X ~ N(50, 16), what is its standard deviation?

    • 2500
    • 4
    • 16
    • 8

  10. For X ~ N(100, 25), what is the z-score corresponding to an x value of 110?

    • 1
    • 10
    • 0.4
    • 2

  11. In any normal distribution with mean mu, what is the value of P(X < mu)?

    • 0.5
    • 0
    • 0.25
    • 1

  12. For X ~ N(20, 9), between which two values do approximately 95% of observations lie?

    • 14 and 26
    • 20 and 29
    • 17 and 23
    • 11 and 29

  13. A normal distribution has a mean of 70 and standard deviation of 5. What is its median?

    • 65
    • 75
    • 350
    • 70

  14. If Z is the standard normal variable, what is the probability P(Z < 0)?

    • -0.5
    • 0.5
    • 0
    • 1

  15. For X ~ N(30, 4), what is the x-value of the upper point of inflection?

    • 38
    • 32
    • 34
    • 30.4

  16. For the standard normal distribution, how is P(Z > a) written using the cumulative function Phi(a)?

    • Phi(-a) - 1
    • 1 + Phi(a)
    • Phi(a)
    • 1 - Phi(a)

  17. If X ~ N(mu, sigma^2) and P(X < 12) = 0.5, what is the value of mu?

    • 0
    • 24
    • 12
    • 6

  18. For X ~ N(50, 100), what is the standardized z-score for an x value of 35?

    • -1.5
    • -0.15
    • -15
    • 1.5

  19. In a histogram representing a normal distribution, what parameter determines the peak location?

    • Variance
    • Standard deviation
    • Mean
    • Range

  20. For the standard normal variable Z, if P(Z < z) = 0.975, what is z?

    • 1.96
    • 2.576
    • 2.326
    • 1.645

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