It is known that math SAT scores in the entire US population (in 2007) have an average of 510 with a standard deviation of 100. There is a random sample of 50 students.

1. Can you find the probability that the average math SAT score of the sample is below 540?
2. (If yes, find the probability and if no, explain why you can not.)

1. Can you find the probability a randomly selected SAT-taker scores above 550 on math?
2. (If yes, find the probability and if no, explain why you can not.)