The expected value and the standard deviation of the points per game for the player is -6.5 and 65.43 respectively.
Given:
In a certain computer card game, the player is awarded 5 points for each card that is moved to a correct position. The player is penalized 10 points for each minute the game is played. Let the random variable X represent the number of cards moved to a correct position, and let the random variable Y represent the number of minutes the game is played.
From the given table:
E ( X ) = 9.5 * 5 points
= 47.5
E ( Y ) = 5.4 * - 10
= -54
E ( X + Y ) = 47.5 + ( -54 )
= 47.5 - 54
= -6.5
SD ( X ) = 12.5 * 5
= 64.5
SD ( Y ) = - 11
SD ( X + Y ) = [tex]\sqrt{64.5^2 + (-11)^2}[/tex]
= 65.43
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Full question:
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