question is attached

2. (19 points) Your friend offers for you to play a gambling game. A random number z will be generated, where z is normally distributed with mean 0 and variance 1. Your friend then pays you $22. For example, if z = 3, you will get paid $9. (a) (6 points) Your friend offers to play the game in exchange for you paying him $2. Is this a good bet? (In other words, is the expected payment greater than or equal to what you have to pay?) (b) (6 points) Your friend proposes the following modication. He will generate two random numbers, and you will get paid the sum of the two payoffs. That is, you will get a payment of Note that each random number is independent. What must the cost of the game be in order for you to have an expected payoff of zero? (c) (7 points) If the cost of the game is $7.79, what is the minimum number of times a random number must be generated in order for you to have a 90% chance of making money on the game