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2 marksSampling Distribution and Estimation

CAPE Applied Mathematics Unit 1 · 2010 · Paper 2 · Question 5(a)

A random variable X is normally distributed with mean μ and standard deviation 0.19. A sample of size n is taken and the sample mean X̄ is calculated.

State the distribution of X̄ giving its parameters.

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  1. 5(b)(i)Calculate the value of X̄.[4 marks]
  2. 5(b)(ii)Calculate the number of observations taken, n.[4 marks]
  3. 5(c)If 20 independent samples, EACH of size n, are drawn from a distribution and the 90% confidence interval is calculated for EACH, how many of these intervals…[2 marks]
  4. 5(d)(i)a)Calculate an unbiased estimate of the population mean.[3 marks]
  5. 5(d)(i)b)Calculate an unbiased estimate of the population standard deviation.[5 marks]
  6. 5(d)(ii)Construct a 94% confidence interval for the mean amount of money spent by the students at the bookstore.[5 marks]

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