2026 NORTHBROOKS P2 Q3

2026 NORTHBROOKS P2 Q3

Secondary 4
8 marks

A bakery recorded the masses of a batch of 300 cookies.

The cumulative frequency diagram represents the distribution of the masses of the cookies.

  1. Use the curve to estimate
    1. the median mass,[1]
    2. the interquartile range,[2]
    3. the 10th percentile of the cookies.[1]
  2. A cookie is labelled as ‘Medium’ if its mass is greater than or equal to 50 g but less than 56 g.
    Two cookies are chosen at random.
    Calculate the probability that both are ‘Medium’ cookies.[2]
  3. The masses of a second batch of 300 cookies were also recorded.
    The box-and-whisker diagram shows the distribution of the mass.
    Make two comments comparing the masses of the cookies in the two batches.
    Use figures to support your answer.[2]

Solution:

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Answer:(a)(i) \(48\text{ g}\) (ii) \(6.5\text{ g}\) (iii) \(40\text{ g}\). (b) About \(16/345\), or \(59/1495\) using the alternative accepted graph reading. (c) First batch: higher median, smaller IQR.

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