a) A particular treatment is effective in 80% of cases. The treatment is given to 5 patients. What is the probability that the treatment will be effective for exactly 4 of the patients? For at least 4 of the patients? What is the probability that the treatment will be effective for 2 or fewer cases?

b) Suppose 20% of individuals exposed to a particular contaminant develop a certain condition. For a group of 200 exposed individuals, what is the probability that at least 30 develop the condition? What is the probability that between 30 and 40 (inclusive) develop the condition? For these calculations, use the normal approximation to the binomial distribution.