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An orchard harvests apples to be sold in crates. The weight of a single apple varies due to natural conditions.
Based on previous harvests, the weight of an apple has a mean \(\mu = 150\) g and a standard deviation \(\sigma = 10\) g.
A crate contains \(n=40\) apples. Let \(X_i\) be the random variable representing the weight of the \(i\)-th apple in the crate.
  1. Define the random variable \(X_i\) in this context (what does it measure?).
  2. State the expected value and standard deviation of a single variable \(X_i\).
  3. What does the sum \(S_{40} = \sum_{i=1}^{40} X_i\) represent in this context?

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