Exercise 4.41 (p. 153 of the 5th edition) An experiment is conducted to test the effect of an anticoagulant drug on rats. A random sample of 4 rats is employed in the experiment. If the drug manufacturer's claim that 80% of rats given the drug will be favorably affected by the drug is indeed true, answer the following questions. First, define the Binomial random variable X as the number of rats favorably affected out of a random sample of 4 rats. Then X is distributed as the Binomial R.V. with the distribution Bin(4, 0.8) (i) What is the probability that none of the 4 rats will be favorably affected? 4 0 4 P(X=0)= (0.8) (1 − 0.8) = 1 × 1 × 0.0016 = 0.0016 0 (ii) What is the probability that one of the 4 rats will be favorably affected? 4 1 3 P(X=1)= (0.8) (1 − 0.8) = 4 × 0.8 × 0.008 = 0.0256 1 (iii) What is the probability that one or fewer of the 4 rats will be favorably affected? P(X ≤ 1) = P(X=0 or X=1) = P(X=0)+ P(X=1) = 0.0016 + 0.0256 = 0.0272 (iv) How many of 100 rats given the drug would you expect to be favorably affected? What property of X are you using ? In this case, X is distributed as Bin(100,0.8) Expected value of X = E(X) = nπ = 100 × 0.8 = 80