Discuss the below:
According to a recently conducted survey, 90% of all drivers in Trinidad and Tobago claim to consistently driver over the legal speed limit. Assume that this result is true for the current population of the Cayman Islands. Find the probability that, in a random sample of 20 drivers:
1. None of them drive over the legal limit
2. Exactly 5 of them drive over the legal limit
3. At least 2 of them drive over the legal speed limit
4. 19 of them DO NOT drive the legal limit
5. Find the mean
6. Find the variance