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4 marksSampling Distribution and Estimation

CAPE Applied Mathematics Unit 1 · 2017 · Paper 2 · Question 5(b)

A certain supermarket found that the price codes on some packages were not clear. In a random sample of 80 packages, 18 had price codes that were not clear. Construct a 97% confidence interval for the proportion of packages whose price codes were not clear.

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  1. 5(a)A random sample of 55 sweets was found to have a mean mass of 0.93 g and a standard deviation of 0.10 g. Determine an approximate 99% confidence interval for…[4 marks]
  2. 5(c)A random variable X follows a normal distribution with mean, μ, and an unknown variance, σ². A random sample of 150 observations of X gave ∑x = 1600 and ∑x² =…[6 marks]
  3. 5(d)Forty random samples of 5 soap bars are taken and a 90% confidence interval for the mean mass, μ, is calculated for EACH sample. Find the expected number of…[2 marks]
  4. 5(e)(i)State the distribution of X̄, giving its parameters.[4 marks]
  5. 5(e)(ii)Calculate P(X̄ > 4.75).[5 marks]

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