Normal population, known parameters

Questions where the population is stated to be normally distributed (or the variable itself is normal) and both mean and standard deviation are given, requiring direct application of sampling distribution without CLT justification.

1 questions · Moderate -0.3

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Pre-U Pre-U 9795/2 2013 June Q2
9 marks Moderate -0.3
2
  1. The heights of boys in Year 9 are normally distributed with mean 156 cm and standard deviation 8 cm . The heights of girls in Year 10 are, independently, normally distributed with mean 160 cm and standard deviation 7 cm . Find the probability that the mean height of a random sample of 9 boys in Year 9 exceeds the mean height of a random sample of 16 girls in Year 10.
  2. State why the distributions of the sample means are normally distributed.