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A customer is choosing between two financial options for a \(\dollar 1000\) investment over one year. The random variables \(X\) and \(Y\) represent the gain (in dollars) for Option A and Option B, respectively, with:
  • Expected gain: \(E(X) = 67.5\) for Option A and \(E(Y) = 120\) for Option B
  • Standard deviation: \(\sigma(X) = 16.01\) for Option A and \(\sigma(Y) = 95.39\) for Option B
The customer wants to maximize profit regardless of the risk. Which option should they choose, and why? Justify your answer based on the given expected gains and standard deviations.
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