It is known that 76% of new Pod coffee makers operate properly when purchased. Suppose we took a random sample of n=32 new Pod coffee makers. Let X = the number of these selected coffee makers that operate properly. (Do not use a normal approximation for this problem. This is a binomial problem.)

a) What is the probability that X < 21?

b) What is the probability that 23X25?

c) What is the probability that X = 24?

d) What is the expected value of X?

e) What is the variance of X?

f) Copy your R script for the above into the text box here.