A drug is known to control hypertension in eighty percent of the patients who us

Question

A drug is known to control hypertension in eighty percent of the patients who use it Suppose fifteen patients are to take this drug, and let X be the number of patients whom the drug is effective for (a) Find the probability that it is effective for exactly ten patients (b) Find the probability that it is effective for at least fourteen patients (c) Find E(X) and V(X).

Explanation / Answer

This is a Binomial Distribution with p = probability that the drug is effective on a patient p = 0.80 n = number of patients = 15 P(X = x) = nCxpx(1-p)n-x P(X = x) = 15Cx0.8x0.215-x a) To find P(drug is effective for exactly 10 patients) = P(X=10) = 15C10(0.8)100.215-10 = 0.1032 P(drug is effective for exactly 10 patients) = 0.1032 b) To find P(drug is effective for atleast 14 patients) = P(X>=14) = P(X=14) + P(X = 15) = 15C14(0.8)140.215-14 + 15C15(0.8)150.215-15 = 0.132 + 0.035 = 0.1671 P(drug is effective for atleast 14 patients) = 0.1671 c) E(X) = np for a binomial distribution E(X) = 15 x 0.8 = 12 E(X) = 12 V(X) = np(1-p) for a binomial distribution V(X) = 15 x 0.8 x 0.2 V(X) = 2.4

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