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A large battery pack is built by connecting 50 individual cells in series. The pack fails as soon as one cell fails, but for capacity calculation, we consider the total energy.
Let \(X_i\) be the energy capacity of a single cell (in Wh). The manufacturer states that \(\mu = 10\) Wh and \(\sigma = 1\) Wh.
Let \(S_{50}\) be the total energy capacity of the pack.
  1. Find the expected total capacity of the pack, \(E(S_{50})\).
  2. Find the standard deviation of the total capacity, \(\sigma(S_{50})\).
  3. Can we assume the total capacity \(S_{50}\) is normally distributed? Explain.
  4. The pack is sold as a "500 Wh" battery. Find the probability that a pack actually has less than 490 Wh of capacity.

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