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3 marksDiscrete Random Variables

CAPE Applied Mathematics Unit 2 · 2018 · Paper 2 · Question 4(a)(ii)

The mass of a biscuit follows a normal distribution with mean 50 g and standard deviation 4 g. A packet contains 10 biscuits. Packaging material has a mean of 40 g and standard deviation 3 g, independent of the biscuits.

Write a distribution, T, for the total mass of the package of biscuits.

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  1. 4(a)(i)Write a distribution, V, for the total mass of the 10 biscuits.[4 marks]
  2. 4(a)(iii)Calculate the probability that the total mass of the package of biscuits is less than 510 g.[8 marks]
  3. 4(b)(i)Complete the table to show the expected frequency for each day, assuming that haircuts are the same on each day.[2 marks]
  4. 4(b)(ii)Carry out a goodness-of-fit analysis to test the hypothesis that the number of haircuts is the same for each day, using a 10% level of significance. Show full…[8 marks]

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