Assume the probability that a patient recovers from a rare disease is p=0.75. Assume 700 individuals are known to have contracted the disease. Let X denote the discrete random variable that counts the number of these patients who have failed to recover from this disease.

a) Precisely explain why X is a binomial random variable. In particular, how many independent trials are there? What denotes a success on a trial? What is the probability of success on a trial?

b) Setup, but do not explicitly calculate, the probability that less than or equal to 150 people die of this disease.

c) Using the normal approximation to the binomial distribution, compute the approximate probability that less than or equal to 150 people die of this disease