Lesson N2

N2 The Normal distribution Quiz: AQA Maths, Unit 11

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson N2, The Normal distribution: 20 multiple choice questions for the AQA Maths (7357), Unit 11: Statistics, written with Revision Ninja.

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The 20 questions

  1. The Normal distribution is symmetric about which value?

    • Its variance
    • Its standard deviation
    • Its mean
    • Zero, always

  2. Where are the points of inflection of a Normal curve with mean mu and standard deviation sigma?

    • At mu only
    • At mu - 2 sigma and mu + 2 sigma
    • At mu - sigma^2 and mu + sigma^2
    • At mu - sigma and mu + sigma

  3. Which expression standardises a Normal variable X ~ N(mu, sigma^2)?

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

  4. Which statement describes X ~ N(mu, sigma^2)?

    • It has mean mu and standard deviation sigma^2
    • It has mean sigma^2 and variance mu
    • It has mean mu and variance sigma^2
    • It has mean sigma and variance mu

  5. What is the total area under the probability density curve of a Normal distribution?

    • 1
    • 0.5
    • 0
    • 100

  6. Which pair describes the standard Normal distribution Z ~ N(0, 1)?

    • Mean 0 and variance 0
    • Mean 0 and variance 1
    • Mean 1 and variance 0
    • Mean 1 and variance 1

  7. If Z ~ N(0, 1), what is P(Z < 1), to four decimal places?

    • 0.8413
    • 0.1587
    • 0.6826
    • 0.9772

  8. If Z ~ N(0, 1), what is P(Z > 2), to four decimal places?

    • 0.9772
    • 0.0456
    • 0.5000
    • 0.0228

  9. X ~ N(50, 16). What is P(X < 54), to four decimal places?

    • 0.9772
    • 0.8413
    • 0.1587
    • 0.5000

  10. X ~ N(100, 225). What is P(X > 115), to four decimal places?

    • 0.3173
    • 0.8413
    • 0.1587
    • 0.0228

  11. X ~ N(20, 25). What is P(15 < X < 25), to four decimal places?

    • 0.9544
    • 0.6826
    • 0.1587
    • 0.3413

  12. Bags of sugar have masses X ~ N(500, 16) in grams. What is P(X < 492)?

    • 0.9772
    • 0.5000
    • 0.0228
    • 0.1587

  13. Scores X ~ N(60, 100) have standard deviation 10. Approximately what score is the 90th percentile?

    • 66.0
    • 72.8
    • 84.0
    • 75.0

  14. X ~ N(mu, sigma^2). What is P(X < mu)?

    • sigma
    • 0.5
    • 0
    • 1

  15. Given P(Z < 1.645) = 0.95, what is P(Z > -1.645)?

    • 0.90
    • 0.95
    • 0.10
    • 0.05

  16. X ~ N(mu, sigma^2) with P(X < 60) = 0.5 and P(X < 70) = 0.8413. What is sigma?

    • 10
    • 20
    • 1
    • 5

  17. X ~ N(mu, 1). If P(X < 12) = 0.9772, what is mu?

    • 12
    • 2
    • 10
    • 11.5

  18. Which mean and standard deviation give a Normal approximation to B(100, 0.5)?

    • Mean 100, standard deviation 0.5
    • Mean 50, standard deviation 25
    • Mean 50, standard deviation 5
    • Mean 0.5, standard deviation 5

  19. X ~ N(50, 25). Using a continuity correction, approximately what is P(X <= 52)?

    • 0.7257
    • 0.5000
    • 0.6915
    • 0.6554

  20. Two Normal curves have the same mean. Compared with the curve having the smaller standard deviation, the curve with the larger standard deviation is:

    • Narrower and taller
    • Wider and flatter
    • Shifted to the right
    • Still centred at zero but taller

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