Lesson 2.04e

2.04e 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, 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
    • Variance
    • Standard deviation

  2. For the standard normal distribution Z, what are the mean and variance?

    • mean 0 and variance 0
    • mean 1 and variance 0
    • mean 0 and variance 1
    • mean 1 and variance 1

  3. Which transformation converts X ~ N(mu, sigma^2) into the standard normal variable Z?

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

  4. In a normal distribution, approximately what proportion of values lie within one standard deviation of the mean?

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

  5. In a normal distribution, approximately what proportion of values lie within two standard deviations of the mean?

    • about 68%
    • about 99.7%
    • about 75%
    • about 95%

  6. Where do the points of inflection of a normal curve occur?

    • at x = mu +/- 2 sigma
    • at x = mu +/- sigma^2
    • at x = mu +/- sigma
    • at x = 0 only

  7. For a normal variable X ~ N(mu, sigma^2), what is the value of P(X < mu)?

    • 0.25
    • 1
    • 0
    • 0.5

  8. X ~ N(50, 16). Find P(X < 54) to 4 decimal places, using Z = (X - 50)/4 and the standard normal table or calculator.

    • 0.8413
    • 0.9772
    • 0.1587
    • 0.5000

  9. X ~ N(20, 25). Find P(X > 25) to 4 decimal places.

    • 0.3413
    • 0.1587
    • 0.0228
    • 0.8413

  10. X ~ N(100, 9). Find P(94 < X < 103) to 4 decimal places.

    • 0.0228
    • 0.8185
    • 0.8413
    • 0.9545

  11. X ~ N(40, 36). Find the value k such that P(X < k) = 0.9, giving k to 1 decimal place.

    • 47.7
    • 44.3
    • 52.4
    • 49.9

  12. X ~ N(12, 4). Find P(10 < X < 14) to 4 decimal places.

    • 0.4772
    • 0.3413
    • 0.6827
    • 0.9545

  13. A machine fills bags with mass X ~ N(500, 9) grams. A bag is rejected if its mass is below 494 g or above 506 g. Find the probability that a bag is rejected.

    • 0.0455
    • 0.0228
    • 0.9545
    • 0.0910

  14. X ~ N(mu, sigma^2) with P(X < 12) = 0.1 and P(X < 20) = 0.9. Find mu and sigma, giving sigma to 2 decimal places.

    • mu = 16, sigma = 3.12
    • mu = 14, sigma = 3.12
    • mu = 16, sigma = 1.56
    • mu = 16, sigma = 6.25

  15. X ~ N(mu, sigma^2) has P(X > 70) = 0.1587 and mu = 60. What is sigma?

    • 14.1
    • 10
    • 5
    • 100

  16. About which statistic is a normal distribution curve perfectly symmetrical?

    • Variance
    • Mean
    • Range
    • Standard deviation

  17. If X ~ N(30, 4), what is the value of P(X = 30) in a continuous normal distribution?

    • 1
    • 0
    • 0.25
    • 0.5

  18. A normal model is used for the heights of a population with mean 170 cm and standard deviation 8 cm. Approximately what proportion of people are taller than 186 cm?

    • about 84%
    • about 0.5%
    • about 2.5%
    • about 16%

  19. X ~ N(60, 25). Find the value of a such that P(X > a) = 0.0228, giving a to 1 decimal place.

    • 70.0
    • 62.5
    • 65.0
    • 75.0

  20. Which property of a normal distribution makes it unsuitable for strongly skewed data?

    • Continuity
    • Unimodality
    • Symmetry
    • Infinite domain

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