1. [6 marks] Consider a play of the casino game 'Quick Draw'. In this game, the player pays $10 to play. He/she picks one card from the standard deck of 52 cards (i.e. four A's, foul K's, etc.). If the player selects an "A", he/she wins $50 (i.e. the profit is $40); if the player selects a "K", he/she wins $30 (i.e. the profit is $20). Otherwise, the player wins nothing and also loses the bet of $10. Let the random variable X represent the player's profit on a single play of 'Quick Draw'. a) Construct the probability distribution for the random variable X. [3 marks] b) What is the probability that the player makes money on a single play of the game? [1 mark] c) Calculate the expected value of the random variable X and provide an interpretation of its value in the context of the question. [2 marks] 2. [6 marks] New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $204 per night. Assume that room rates are normally distributed with a standard deviation of $55. a) What is the probability that a hotel room costs between $200 and $300 per night? [3 marks] b) What is the cost of the 20% most expensive hotel rooms in New York City? [3 marks]