Miguel is a brand manager facing a difficult decision. The top two candidates for his brand's next major product initiative all seem quite likely to be successful, but due to budget constraints, he must select only one. He has asked you to provide an analysis of the different initiatives to inform his selection decision. The following is information related to each of the initiatives:

Initiative 2

• The development cost depends on the state of its development team. With probability 0.80, the assigned development team is strong and thus the cost is normally distributed with a mean of $1 million and a standard deviation of $100,000. With probability 0.20, the assigned development team is weak and thus the cost is normally distributed with a mean of $2 million and a standard deviation of $500,000.
• The firm has much more discretion on pricing. There are 220 potential clients for the product, and each one will purchase it with probability (p) which depends on the price p. This probability function is given by (p) = 1 p $100,000. Here the highest price that can be charged is $100,000, and it will lead to no customers purchasing it.

1. For Initiative 2, what is the likelihood that its cost exceeds $2.5 million?
2. For Initiative 2, if the price is set to $30,000, what is the expected profit?