chapter 1

Chapter 3: Discrete Random Variables and Probability Distributions54. Let p denote the actual proportion of defectives in the batch, and X denote the number ofdefectives in the sample.a. P(the batch is accepted) = P(X ≤ 2) = B(2;10,p)p .01 .05 .10 .20 .25P(accept) 1.00 .988 .930 .678 .526b.1.0P(accept)0.50.00.00.10.20.30.40.50.60.70.80.91.0pc. P(the batch is accepted) = P(X ≤ 1) = B(1;10,p)p .01 .05 .10 .20 .25P(accept) .996 .914 .736 .376 .244d. P(the batch is accepted) = P(X ≤ 2) = B(2;15,p)p .01 .05 .10 .20 .25P(accept) 1.00 .964 .816 .398 .236e. We want a plan for which P(accept) is high for p ≤ .1 and low for p > .1The plan in d seems most satisfactory in these respects.110