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2 marksProbability, Probability Distributions and Regression

CAPE Integrated Mathematics · 2016 · Paper 2 · Question 4(d)(i)

The mass of barrels arriving in a specific country follows a normal distribution with mean 140 kg and standard deviation 5 kg. Show that the z-value of a barrel of mass 132 kg is z = -1.6.

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Other parts of this question

  1. 4(a)(i)Find, to the nearest whole number, the value of a.[2 marks]
  2. 4(a)(ii)Find, to the nearest whole number, the value of b.[2 marks]
  3. 4(b)(i)Determine the median time.[1 mark]
  4. 4(b)(ii)Find the lower quartile time.[2 marks]
  5. 4(b)(iii)Using the axis provided, construct a box-and-whisker plot for the time spent completing the job, given that the upper quartile is 25 minutes.[3 marks]
  6. 4(c)(i)Given that X ~ Bin(n, 0.4) where the mean is 3.2, show that the number of trials, n = 8.[2 marks]
  7. 4(c)(ii)Find P(X >= 6).[4 marks]
  8. 4(d)(ii)Find the probability that a barrel selected at random weighs more than 132 kg.[4 marks]
  9. 4(e)(i)On the grid provided on page 19, draw a scatter plot to represent the data.[2 marks]
  10. 4(e)(ii)Briefly comment on the shape of the scatter plot.[1 mark]

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