Assume the daily minimum temperature for Boston in January is independently and normal distribution with mean = -10C, and a standard deviation of 3 C.

Some people like to skate on Lake. I understand that if the ice is not safe to skate on, it will freeze hard enough to allow people to skate on it safely if the minimum temperature is below -8C for at least five days in a row. Once safely frozen, it will stay that way as long minimum daily temperature remains below -5C. If temperature gets higher it becomes dangerous.

The minimum temperature on New Year's Eve (Dec 31) was -6C and the ice was not safe for skating.

1. What it the probability that we can skate safely on the morning of January 6?
2. Assuming we were able to safely skate on the morning of Jan 6, what is the probability we will be able to skate on the morning of Jan 9?