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Statistical inference — Question 18

QCAA 2020, Paper 2 · 6 marks

Q18 · 2020 · Technology-activeComplex unfamiliar6 marks

QUESTION 18 (6 marks)

The mass of a certain species of kangaroo is known to be normally distributed with a mean mass of μ\mu kg and standard deviation of σ\sigma kg. When one kangaroo is randomly selected, P(X>83.2)=0.145P(X>83.2)=0.145. When a sample of 12 kangaroos is randomly selected, P(Xˉ<74.1)=0.079P(\bar X<74.1)=0.079. A 90% approximate confidence interval for μ\mu is calculated using a random sample of nn kangaroos with sample mean 79.1 kg and sample standard deviation equal to σ\sigma. Determine the possible range of values that nn could have been, given that the confidence interval did not contain μ\mu.
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