In the Healthy Handwriting Survey conducted by Bradley Corporation, it was found that 64% of adult Americans operate the flusher of toilets in public restrooms with their foot. Suppose a random sample of n=20 adult Americans is obtained and the number X who flush their public toilets with their foot id recorded.

a) Identify the distribution of the random variable X. Give parameters of the distribution
b) Find the probability that exactly 12 flush public toilets with their foot
c) Find the probability that between 9 and 11, inclusive, flush public toilets with their foot
d) Find the probability that less than or equal to 2 flush public toilets with their foot. Based on the probability, is it an unusual event?
e) Compute the mean and standard deviation of the random variable X