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A biologist is planning a study to measure the weight of 10 penguins.
  1. Planning Phase: She writes a formula to calculate the average weight she expects to find: \(\frac{X_1 + X_2 + \dots + X_{10}}{10}\). Explain why she uses uppercase \(X\).
  2. Data Analysis Phase: She measures the penguins and gets the list: \(\{12.5, 11.8, 13.2, \dots\}\). She calculates the average: \(\frac{x_1 + x_2 + \dots + x_{10}}{10} = 12.4\). Explain why she uses lowercase \(x\).
  3. Which of the two averages is the Estimator (\(\overline{X}\)) and which is the Estimate (\(\bar{x}\))?

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