1. Suppose that you have the opportunity to win a prize by playing a game of chance during the Statistics Department's Applied Probability Night. To play, you can choose one of the following:

• Option A: Draw five random numbers from a normal distribution centered at 102 with standard deviation 3. Your score equals the sum of numbers drawn.
• Option B: Draw one random number from a normal distribution centered at 102 with standard deviation 2.5. Your score equals the number drawn multiplied by five.

You win a prize if your score is greater than 520. Which option should you choose to maximize your chance of winning a prize?

If using an algebraic approach, explain your reasoning and clearly define any notation used. If using a simulation approach, be sure to briefly describe the logic used to write the simulation and clearly comment your solution code.