\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
The random variables \(X_1, X_2, \dots, X_6\) represent the weight of a cookie, each with a mean of \(30 \mathrm{~g}\) and a standard deviation of \(2 \mathrm{~g}\). We assume the weights are independent.The random variable \(S_6 = X_1 + X_2 + \dots + X_6\) represents the total weight of a packet of 6 cookies.
  1. Find the expected total weight (mean) of the packet, \(E(S_6)\).
  2. Find the standard deviation of the total weight of the packet, \(\sigma(S_6)\).

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