Quelpr
5 marksSampling Distribution and Estimation

CAPE Applied Mathematics Unit 1 · 2016 · Paper 2 · Question 5(b)

The mean of 150 observations of X, where X ~ Bin(135, 0.36) is X̄. Use the central limit theorem to state the distribution that is modelled by X̄, giving the values of its parameters.

The mark scheme is shown once you've answered.

Practise this question

Other parts of this question

  1. 5(a)(i)Calculate unbiased estimates for the population mean, µ.[2 marks]
  2. 5(a)(ii)Calculate unbiased estimates for the standard deviation, σ, of the length of time between planting and germination.[3 marks]
  3. 5(a)(iii)Construct a 94% confidence interval for the mean length of time it takes for this type of pepper seed to germinate.[3 marks]
  4. 5(a)(iv)Sixty random samples of 49 pepper seeds are taken and a 95% confidence interval for µ is found for each sample. Determine the appropriate number of intervals…[2 marks]
  5. 5(c)(i)State, in symbols, appropriate null and alternative hypotheses for the test.[3 marks]
  6. 5(c)(ii)Determine the critical region(s) for the test.[3 marks]
  7. 5(c)(iii)Calculate the value of the test statistic.[2 marks]
  8. 5(c)(iv)State your conclusions, giving reasons.[2 marks]

More practice: the rest of this paper · more Sampling Distribution and Estimation questions · all CAPE Applied Mathematics Unit 1 past papers