Lesson 2.04f

2.04f Calculator use with the normal distribution Quiz: OCR Maths, Unit 14

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 2.04f, Calculator use with 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. What are the mean and variance of the standard normal distribution Z?

    • Mean 1, variance 1
    • Mean 0, variance 0
    • Mean 0, variance 1
    • Mean 1, variance 0

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

    • Z = (X - μ) / σ²
    • Z = (X - μ) / σ
    • Z = (X - σ) / μ
    • Z = (μ - X) / σ

  3. At which values of x do the points of inflection occur on a normal curve?

    • x = μ ± σ²
    • x = μ ± 2σ
    • x = μ ± σ
    • x = μ ± 3σ

  4. Approximately what percentage of values in a normal distribution lie within one standard deviation?

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

  5. What proportion of data lies within two standard deviations of the mean in a normal distribution?

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

  6. Which calculator menu option is used to calculate P(a < X < b) for a normal variable?

    • Normal CD
    • Inverse Normal
    • Binomial CD
    • Normal PD

  7. Which calculator function finds the value x when cumulative probability P(X < x) is given?

    • Normal PD
    • Binomial PD
    • Normal CD
    • Inverse Normal

  8. For the distribution X ~ N(50, 16), what is the value of the standard deviation σ?

    • 2500
    • 4
    • 8
    • 16

  9. Calculate the Z-score for X = 15 when the mean is 10 and standard deviation is 2.5.

    • 2
    • 5
    • -2
    • 1.5

  10. If a normal distribution has mean 100 and standard deviation 15, where are its inflection points?

    • 50 and 150
    • 90 and 110
    • 85 and 115
    • 70 and 130

  11. What is the probability P(Z < 0) for the standard normal distribution Z ~ N(0, 1)?

    • 0.5
    • 1
    • 0.25
    • 0

  12. If P(X < x) = 0.5 for X ~ N(20, 9), what is the value of x?

    • 3
    • 9
    • 20
    • 0

  13. Calculate the Z-score for X = 8 when the mean is 12 and standard deviation is 2.

    • -1
    • -4
    • 2
    • -2

  14. Almost all values in a normal distribution lie within how many standard deviations of the mean?

    • 2
    • 4
    • 3
    • 1

  15. What parameter represents the centre of symmetry in the normal distribution model N(μ, σ²)?

    • Standard deviation
    • Variance
    • Range
    • Mean

  16. For X ~ N(10, 4), what is the value of P(X > 10)?

    • 0
    • 1
    • 0.25
    • 0.5

  17. Using the empirical rule for X ~ N(50, 25), what value of x gives P(X > x) ≈ 0.025?

    • 65
    • 60
    • 55
    • 75

  18. What shape characterises the graph of a normal probability density function?

    • Uniform rectangle
    • Symmetrical bell shape
    • Skewed right curve
    • U-shaped curve

  19. How does increasing standard deviation alter a normal curve with fixed mean?

    • Shifts to the left
    • Flattens and widens
    • Shifts to the right
    • Tallies and narrows

  20. Which parameter represents the scale or spread of values in a normal distribution model?

    • Median
    • Mean
    • Mode
    • Standard deviation

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