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4MA1/2H Jan 2021, Question 15: Histograms (Unequal Class Intervals)

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 6 marks

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The question, in short

Use the histogram of parcel weights, with 63 parcels in the 0.5 kg to 2 kg class, to find the total number of parcels and a probability for two randomly chosen records.

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

Part (a) · 3 marks

Using the 63 parcels in the 0.5 kg to 2 kg class, work out the total number of parcels delivered last Monday.

  1. 1Frequency density for 0.5−2 kg = 63 ÷ 1.5 = 42, so 1 small square = 1 unit
  2. 2Other bars: 0.5 × 18 = 9, 1 × 24 = 24, 1 × 30 = 30, 2 × 8 = 16
  3. 3Total = 9 + 63 + 24 + 30 + 16 = 142

Answer142

Part (b) · 3 marks

Estimate the probability that both randomly picked records are parcels weighing more than 2.25 kg.

  1. 1Parcels over 2.25 kg: 0.75 × 24 = 18, then 18 + 30 + 16 = 64
  2. 2There are 142 parcels: first pick 64/142, second pick 63/141
  3. 3P = 64/142 × 63/141 = 4032/20022
  4. 4Simplify: 672/3337

Answer672/3337

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