Produce the probability histogram (probability distribution plot) of each of the following and state if the distribution is symmetric, skewed to the left, or skewed to the right. The binomial distribution with n = 20 and p = 0.2.

The binomial distribution with n = 30 and p = 0.48

The binomial distribution with n = 15 and p = 0.8.

Suppose X is a binomial random variable with n = 35 and p = 0.67.

What is the probability that X is exactly 20?

What is the probability that X is at most 27?

What is the probability that X is at least 15?