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A consumer group tests the lifespan of 50 randomly selected tires of a specific brand. The sample mean lifespan is \(42,000\) km and the sample standard deviation is \(s_n = 4,000\) km.
  1. Explain why the normal distribution can be used to construct the confidence interval even though the population variance is unknown.
  2. Calculate the \(95\pourcent\) confidence interval for the mean lifespan of the tires.

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