Question: A member of a family of 6 randomly chooses and makes 3 boxes of pasta from their cupboard containing 2 boxes of linguine, 3 boxes of penne, and 4 boxes of spaghetti. Denote by X the number of boxes of spaghetti chosen.

1. What is the probability that exactly 1 box of spaghetti is made?
2. Find the probability distribution of X.
3. Find the expected value and standard deviation of X.
4. (5 points) Draw the probability distribution of X and mark where the expected value is and one standard deviation away from the mean in both the positive and negative direction.

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