**Learning Goal: **I’m working on a statistics multi-part question and need an explanation and answer to help me learn.

**Instructions:**

This assignment has three questions. The full credits are 20.

**Problem 1 (6 points):**

An analyst estimates that the probability of default on a seven-year AA-rated bond is 0.06, while that on a seven-year A-rated bond is 0.13. The probability that they will both default is 0.04.

- What is the probability that at least one of the bonds defaults? (2 points)
- What is the probability that neither the seven-year AA-rated bond nor the seven-year A-rated bond defaults? (2 points)
- Given the seven-year AA-rated bond defaults, what is the probability that the seven-year A-rated bond also defaults? (2 points)

**Problem 2 (7 points):**

Organizers of an outdoor summer concert are concerned about the whether conditions on the day of the concert. They will make a profit of $25,000 on a clear day and $10,000 on a cloudy day. They will take a loss of $5,000 if it rains. The weather channel has predicted a 60% chance of rain on the day of the concert. Calculate the expected profit from the concert if the likelihood is 10% that it will be sunny and 30% that it will be cloudy.

**Problem 3 (7 points):**

The average rent in a city is $1,500 per month with a standard deviation of $250. Assume rent follows the normal distribution. What percentage of rents are between $1,250 and $1,750?