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Suppose \(X\) represents the high scores (in points) of players in a new battle royale video game, and it follows a normal distribution with a mean of 500 points and a standard deviation of 50 points. Liam gets a high score of 600 points and brags, “I’m in the top 5\(\pourcent\) of all players!”
Are you agree with Liam ? Explains your answer.\FieldText{1}{\(X \sim \mathcal{N}(500, 50^2)\). I calculate:$$P(X \geq 600) \approx 0.023$$I don’t agree. He’s in the top 2.3\(\pourcent\), not 5\(\pourcent\)—he’s even better!}