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A sociologist surveys the daily commute time of workers in a large city.
The population mean commute time is \(\mu = 45\) minutes with a standard deviation \(\sigma = 12\) minutes.
The sociologist selects a random sample of 100 workers. Let \(X_k\) be the random variable representing the commute time of the \(k\)-th worker.
  1. Define the variable \(X_k\). Is it a discrete (Bernoulli) or continuous variable?
  2. Give the mean and standard deviation of a single variable \(X_k\).
  3. Express the sample mean \(\overline{X}_{100}\) in terms of \(X_k\) and explain what it represents.

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