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4MA1/2H Nov 2021, Question 14: Histograms (Unequal Class Intervals)

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 5 marks

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The question, in short

Using a grouped frequency table of minutes late for flights, draw a histogram and estimate a conditional probability for a randomly chosen flight.

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

Part (a) · 3 marks

Draw a histogram on the grid from the grouped frequencies, using unequal class widths.

  1. 1Frequency density = frequency ÷ class width
  2. 28 ÷ 10 = 0.8, 13 ÷ 5 = 2.6, 19 ÷ 10 = 1.9
  3. 324 ÷ 15 = 1.6, 6 ÷ 20 = 0.3
  4. 4Draw bars of these heights over each class

AnswerBars at frequency density 0.8 from 0 to 10, 2.6 from 10 to 15, 1.9 from 15 to 25, 1.6 from 25 to 40, 0.3 from 40 to 60

Part (b) · 2 marks

Estimate the probability that a flight late by 25 minutes or less was late by 5 minutes or less.

  1. 1Late by 25 minutes or less: 8 + 13 + 19 = 40 flights
  2. 25 minutes or less is half of the 0 to 10 class: 8 ÷ 2 = 4
  3. 3Probability = 4/40

Answer4/40

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