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Alex likes to play Trivia Triumph, an online trivia game. In this game, trivia questions are presented and players have up to $30$ seconds to select an answer from a list of $5$ choices. Each question starts at a point value of $300$ points, but $10$ points are deducted for each second it takes the player to answer the question. Therefore, the number of points, $P$, that a player earns on a single question can be described by the following equation


... where $S$ represents the number of seconds it takes the player to select an answer.

Whether he knows the answer to a question or not, Alex tends to answer in about the same amount of time. His online statistics shows that the mean amount of time it takes him to answer a question, ${\mu}_{S}$ is $13.4$ seconds with a variance of $5.29$ seconds.

What is the standard deviation of the number of points Alex earns when he gets a question correct?











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