Of all the registered automobiles in Pennsylvania, 3% fail the state emission test. Twelve automobiles were selected at random to undergo the emission test. Let X be the number of automobiles that fail the emission test out of sampled 12.

1. Does X follow a binomial distribution? Check the four conditions that need to be satisfy in order for X to have a binomial distribution.
2. Calculate the mean and the standard deviation for the random variable X
3. Find the probability exactly 3 of them failing the emission test. Show your work.
4. Would it be unusual for none of the sampled vehicles to fail the emission test? Show calculations relevant to your calculation.