she receives 1,0 6. There is a game in a casino with the following rules. A machine generates a random number X from a normal distribution with mean 100 and standard deviation 10. If X is at least 100 then the player receives the amount X - 100 dollars. If X is below 100 then the player pays 100 - X dollars. Let Y be the amount the player is going to win, with the understanding that Y is negative if the player has to pay. For example, if X = 109 then Y =9, and if X = 95 then Y = -5. (a) What is the expected value of Y? (10 pts.) (b) What is the standard deviation of Y? (c) A player plans to play this game 30 times. What is the probability that at least 5 times out of the 30 games she will win more than 10 dollars? (10 pts.)