CAPE Applied Mathematics Unit 1 · 2015 · Paper 2 · Question 5(b)(ii)
Random variable X has E[X] = 25 and Var[X] = 144. Samples of size 81 are taken from X.
Calculate P(X̄ < 28).
The mark scheme is shown once you've answered.
Practise this questionOther parts of this question
- 5(a)(i)Calculate the width of the interval.[2 marks]
- 5(a)(ii)Calculate the mean of the sample.[2 marks]
- 5(a)(iii)Calculate the standard deviation of the value of the sales invoice.[3 marks]
- 5(b)(i)State the approximate distribution modelled by X̄, giving its parameters.[3 marks]
- 5(c)(i)State null and alternative hypotheses, using statistical symbols to test whether the mean mass has changed.[2 marks]
- 5(c)(ii)Determine the critical region(s) of the test conducted at the 4% significance level.[3 marks]
- 5(c)(iii)Calculate the value of the test statistic used in this test.[3 marks]
- 5(c)(iv)Clearly state the conclusion of the test.[2 marks]
More practice: the rest of this paper · more Sampling Distribution and Estimation questions · all CAPE Applied Mathematics Unit 1 past papers