2025 MGS(S) PRELIMS P2 Q6

2025 MGS(S) PRELIMS P2 Q6

Secondary 4
11 marks
  1. The cumulative-frequency curve shows the speeds of 300 cars passing a road in the morning.
    1. Use the curve to estimate
      1. the median speed,[1]
      2. the interquartile range of the speeds,[2]
      3. the 70th percentile.[1]
    2. Given that 10% of the cars have a speed greater than \(p\text{ km/h}\), find \(p\).[1]
    3. The box-and-whisker plot below shows the afternoon speeds. Make two comments comparing morning and afternoon speeds.[2]
  2. Ten identical cards are labelled 1 to 10. Two are drawn at random without replacement. Find the probability that
    1. both numbers are odd,[1]
    2. one number is odd and the other is even,[2]
    3. the product of the two numbers is even.[1]

Solution:

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Answer:(a)(i)(a) \(29.5\text{ km/h}\) (b) \(7.0\text{ km/h}\) (c) \(32.5\text{ km/h}\) (ii) \(p=38\) (iii) lower median and smaller IQR in morning (b)(i) \(\frac29\) (ii) \(\frac59\) (iii) \(\frac79\)

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