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4024/21 Oct/Nov 2025, Question 17: Grouped mean and probability

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 7 marks

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The question, in short

Race times of 80 people: 20 < t ≤ 30 (20 people), 30 < t ≤ 50 (26), 50 < t ≤ 60 (29), 60 < t ≤ 90 (5). Estimate the mean time, then find a probability for two people chosen at random.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 4 marks

Estimate the mean time.

  1. 1Midpoints: 25, 40, 55, 75
  2. 2Σfx = 20 × 25 + 26 × 40 + 29 × 55 + 5 × 75 = 500 + 1040 + 1595 + 375 = 3510
  3. 3Mean = 3510 ÷ 80 = 43.875 minutes

Answer43.875

Part (b) · 3 marks

Two people are chosen at random. Find the probability that one took 30 minutes or less and the other took more than 60 minutes.

  1. 130 minutes or less: 20 people; more than 60 minutes: 5 people
  2. 2P = 20/80 × 5/79 + 5/80 × 20/79 = 2 × 100/6320
  3. 3= 200/6320 = 5/158

Answer5/158

Stuck on a step? Read the free lesson: Estimating the Mean for Grouped Data

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