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IB Mathematics: Applications and Interpretation HL · 13.2: Probability Distributions · 13.2.15

Probability distributions: exam review Exam review: second paper Answers

Section A: short questions

    1. (a) 0.15
    2. (b) 0.55
    3. (c) 5/16 (0.312)
    1. (a) 0.1
    2. (b) 7/9 (0.778)
    1. (a) \$3.50
    2. (b) −\$1.50; not fair
    3. (c) \$3.50
    1. (a) x = 0: 7/15 (0.467); x = 1: 7/15 (0.467); x = 2: 1/15 (0.0667)
    2. (b) 3/5 (0.6)
    3. (c) 8/15 (0.533)
    1. (a) X ~ B(15, 0.12)
    2. (b) 0.170
    3. (c) 0.974
    4. (d) 0.0959
    1. (a) E(X) = 15, Var(X) = 6
    2. (b) p = 0.25, n = 80
    3. (c) 0.440
    1. (a) Answers are independent; the probability of a correct guess is the same for every question
    2. (b) 0.0726
    3. (c) 0.208
    1. (a) 0.367
    2. (b) 76
    3. (c) 84
    1. (a) 83.85%
    2. (b) 0.0668
    1. (a) 109 mm to 131 mm
    2. (b) lower quartile 114 mm, upper quartile 126 mm
    3. (c) \(\mu = 118\), \(\sigma = 11.2\)

Section B: long questions

    1. (a) 0.159
    2. (b) 0.611
    3. (c) 28.0
    4. (d) 13.7
    5. (e) 0.186
    6. (f) The items are independent of each other, and the probability is the same for each
    7. (g) Mean 6 is less than 2 × 4 = 8, so the model gives a large probability of a negative value
    1. (a) a + b = 0.55
    2. (b) a = 0.25, b = 0.3
    3. (c) 11/16 (0.688)
    4. (d) Expected profit −\$0.40; not fair
    5. (e) 0.146
    6. (f) 0.756
    1. (a) The median is near the middle of the box; the whiskers are about the same length (symmetric)
    2. (b) Q1 = 34.0, Q3 = 42.0
    3. (c) 8.09
    4. (d) 46.4
    5. (e) 44.2
    6. (f) 5.88
    1. (a) The events happen independently of each other; they happen at a constant average rate (or singly)
    2. (b) 0.114
    3. (c) 0.138
    4. (d) 0.456
    5. (e) 2.74
    1. (a) 5 × 3 = 15
    2. (b) Z ~ Po(21)
    3. (c) 0.227
    4. (d) E(Z) = 21, standard deviation = 4.58
    5. (e) Both could depend on the same cause, for example the same weather, event or time of day
    6. (f) T is a time between events, not a number of events in a given period
    1. (a) 2 orders
    2. (b) 1.2
    3. (c) 17

jmaths.xyz · AI HL · 13.2.15 Unit review