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IB Mathematics: Applications and Interpretation SL · 13.2: Probability Distributions · 13.2.11

Probability distributions: exam review Exam review Answers

Section A: short questions

    1. (a) 0.2
    2. (b) 0.35
    3. (c) 12/19 (0.632)
    1. (a) 0.1
    2. (b) 5/9 (0.556)
    1. (a) \$3
    2. (b) −\$1; not fair
    3. (c) \$3
    1. (a) x = 0: 5/18 (0.278); x = 1: 5/9 (0.556); x = 2: 1/6 (0.167)
    2. (b) 8/9 (0.889)
    3. (c) 13/18 (0.722)
    1. (a) X ~ B(20, 0.08)
    2. (b) 0.271
    3. (c) 0.929
    4. (d) 0.212
    1. (a) E(X) = 14, Var(X) = 9.1
    2. (b) p = 0.3, n = 60
    3. (c) 0.437
    1. (a) Answers are independent; the probability of a correct guess is the same for every question
    2. (b) 0.0781
    3. (c) 0.179
    1. (a) 0.46
    2. (b) 59
    3. (c) 62
    1. (a) 81.5%
    2. (b) 0.0228
    1. (a) 52.7 g to 63.3 g
    2. (b) lower quartile 55.8 g, upper quartile 60.2 g
    3. (c) \(\mu = 58.8\), \(\sigma = 3.77\)

Section B: long questions

    1. (a) 0.0912
    2. (b) 0.750
    3. (c) 479
    4. (d) 38.2
    5. (e) 0.174
    6. (f) The items are independent of each other, and the probability is the same for each
    7. (g) Mean 40 is less than 2 × 22 = 44, so the model gives a large probability of a negative value
    1. (a) a + b = 0.5
    2. (b) a = 0.3, b = 0.2
    3. (c) 11/17 (0.647)
    4. (d) Expected profit −\$0.25; not fair
    5. (e) 0.279
    6. (f) 0.831
    1. (a) The median is near the middle of the box; the whiskers are about the same length (symmetric)
    2. (b) Q1 = 36.6, Q3 = 47.4
    3. (c) 10.8
    4. (d) 54.4
    5. (e) 52.3
    6. (f) \$4.06

jmaths.xyz · AI SL · 13.2.11 Unit review