2025 NASS PRELIMS P2 Q4

2025 NASS PRELIMS P2 Q4

Secondary 4
9 marks

A cumulative-frequency curve shows the waiting times of 80 passengers boarding Star Cruise.

  1. Use the curve to estimate
    1. the median waiting time,[1]
    2. the interquartile range of the waiting time,[2]
    3. the percentage of passengers who took at least 30 minutes to board.[2]
  2. Another 80 passengers boarding Diamond Cruise had the same median but a higher interquartile range. Describe how its cumulative-frequency curve would differ.[1]
  3. Two Star Cruise passengers are selected at random. Find the probability that
    1. both waited less than 25 minutes,[1]
    2. one waited less than 25 minutes and the other waited at least 36 minutes.[2]

Solution:

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Answer:(a)(i) \(28.8\text{ min}\) (ii) \(11.2\text{ min}\) (iii) \(44.4\%\) (b) same median, wider quartile separation (c)(i) \(0.111\) (ii) \(0.120\)

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