3. Frustrated by your loss, you shrug it off and walk over to the Fountains of Bellagio to ponder your choices in life. While gazing into the massive jets of water streaming high into the air, you recall a piece of information you read on the flight into town - that the average person gambling in Las Vegas loses roughly $500 in a given year. Assuming this is correct, and that the average person's losses are roughly Normal with a standard deviation of $300 (and that a person only visits Vegas once in a given year):

a) What is the probability that you will leave Vegas having lost no more than that $100?

b) What is the probability that you will leave Vegas having lost more than $200?

c) What is the probability that you will leave Vegas having more money than you arrived with? d) What proportion of people leave Vegas having lost between $200 and $800 (for a given year)?