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Suppose you have a treatment for a rare disease. If you apply this treatment to a...

Suppose you have a treatment for a rare disease. If you apply this treatment to a person, they have a 32% chance of recovery. Suppose you apply your treatment to twelve patients. Show all work using the formula, do not use software. Let X be the number of patients who recover. (SHOW YOUR WORK)

(a) To ensure that this is a binomial random variable we must assume something about our
trials/ patients. What do we have to assume about our trials (patients) that I did not explicitly state?
Find n and p.
(b) Find the mean and standard deviation of X.
(c) Find the probability that exactly four individuals recover.
(d) Find the probability that at least one patient recovers. (Hint: use the complement rule.)

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