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Quiz Chapter 5: Probability Distribution

10 questions · Form 5 Additional Mathematics Bab 5: Probability Distribution

10 questions · plays in fullscreen

Full Question List & Answer Key

Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.

1. Given Z ~ N(0, 1) and P(Z < k) = 0.8413, find k.

  1. 1.00
  2. -1.00
  3. 0.50
  4. 1.96
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Answer: A

P(Z < k) = 0.8413 => P(Z > k) = 1 - 0.8413 = 0.1587. From normal distribution tables, Z = 1.00.

2. In a fair die roll repeated 180 times, what is the standard deviation of obtaining the number '6'?

  1. 5
  2. 25
  3. 30
  4. 6
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Answer: A

n = 180, p = 16, q = 56. Variance = npq = 180 × (16) × (56) = 25. Standard deviation σ = √25 = 5.

3. If X ~ B(4, 0.5), calculate P(X = 2).

  1. 0.375
  2. 0.250
  3. 0.500
  4. 0.125
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Answer: A

P(X = 2) = ⁴C₂ (0.5)² (0.5)² = 6 × 0.25 × 0.25 = 0.375.

4. A random variable X is binomially distributed with X ~ B(100, 0.2). Find the mean and variance of X.

  1. Mean = 20, Variance = 16
  2. Mean = 20, Variance = 4
  3. Mean = 80, Variance = 16
  4. Mean = 10, Variance = 16
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Answer: A

Mean = np = 100 × 0.2 = 20. Variance = npq = 100 × 0.2 × 0.8 = 16.

5. If X ~ B(n, p) where mean = 15 and standard deviation = 3, find the probability of success p.

  1. 0.4
  2. 0.6
  3. 0.2
  4. 0.8
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Answer: A

Mean np = 15. Standard deviation √npq = 3 => npq = 9. Substituting np = 15 gives 15q = 9 => q = 0.6. Thus, p = 1 - 0.6 = 0.4.

6. Given that X ~ B(n, p) has mean = 12 and variance = 3. Find the values of n and p.

  1. n = 16, p = 0.75
  2. n = 16, p = 0.25
  3. n = 24, p = 0.50
  4. n = 12, p = 0.75
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Answer: A

np = 12 and npq = 3. Substituting np = 12 into npq gives 12q = 3 => q = 0.25. So p = 1 - 0.25 = 0.75. Then n(0.75) = 12 => n = 16.

7. A continuous random variable X is normally distributed with mean 50 and standard deviation 5. Find the Z-score when X = 62.5.

  1. 2.5
  2. 12.5
  3. 2.0
  4. 1.5
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Answer: A

Z = (X - μ) / σ = 62.5 - 505 = 12.55 = 2.5.

8. The total area under a standard normal probability distribution curve is equal to:

  1. 1.0
  2. 0.5
  3. 100
  4. 2.0
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Answer: A

By definition, the total area under any probability density curve, including the normal curve, is always 1.

9. If X ~ B(5, 0.4), find P(X ≥ 1).

  1. 0.9222
  2. 0.0778
  3. 0.6723
  4. 0.8208
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Answer: A

P(X ≥ 1) = 1 - P(X = 0) = 1 - ⁵C₀ (0.4)⁰ (0.6)⁵ = 1 - 1(1)(0.07776) = 1 - 0.07776 = 0.92224 ≈ 0.9222.

10. In a town, the masses of residents are normally distributed with mean 65 kg and variance 25 kg². Find the percentage of residents with masses between 60 kg and 70 kg.

  1. 68.26%
  2. 95.44%
  3. 50.00%
  4. 34.13%
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Answer: A

μ = 65, σ = √25 = 5. For X = 60, Z1 = 60 - 655 = -1.0. For X = 70, Z2 = 70 - 655 = 1.0. P(-1.0 < Z < 1.0) = 1 - 2(0.1587) = 0.6826 = 68.26%.

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