3-2Solutions Manual for Statistical Inference3.5 LetX= number of effective cases. If the new and old drugs are equally effective, then theprobability that the new drug is effective on a case is.8. If the cases are independent thenX∼binomial(100, .8), andP(X≥85) =100x=85100x.8x.2100-x=.1285.So, even if the new drug is no better than the old, the chance of 85 or more effective cases isnot too small. Hence, we cannot conclude the new drug is better. Note that using a normalapproximation to calculate this binomial probability yieldsP(X≥85)≈P(Z≥1.125) =.1303.3.7 LetX∼Poisson(λ). We wantP(X≥2)≥.99, that is,P(X≤1) =e-λ+λe-λ≤.01.Solvinge-λ+λe-λ=.01 by trial and error (numerical bisection method) yieldsλ= 6.6384.3.8 a. We wantP(X > N)< .01 whereX∼binomial(1000,1/2). Since the 1000 customers chooserandomly, we takep= 1/2. We thus require
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