A manufacturer of integrated circuit chips wishes to control the quality of its product by rejecting any batch in which the proportion of defective chips is too high. To this end, out of each batch (10,000 chips), 25 will be selected and tested. If at least 5 of these 25 are defective, the entire batch will be rejected. a. ?What is the probability that a batch will be rejected if 5% of the chips in the batch are in fact defective? b. ?Answer the question posed in (a) if the percentage of defective chips in the batch is 10%. c. ?Answer the question posed in (a) if the percentage of defective chips in the batch is 20%. d. ?What happens to the probabilities in (a)–(c) if the critical rejection number is increased from 5 to 6?

Answer Step 1 of 5 Given n=25, x=5 The pmf of binomial distribution is P(X)=n cp q n; x=0,1,....,n Step 2 of 5 a)The probability that a batch will be rejected if 5% of the chips in the batch are defective Here p=0.05, q=0.95 P(batch is rejected)=P(x5) =1-P(x<5) =1-P(0)-P(1)-P(2)-P(3)-P(4) =0.0072 Step 3 of 5 b)The probability that a batch will be rejected if 10% of the chips in the batch are defective Here p=0.1, q=0.9 P(batch is rejected)=P(x5) =1-P(x<5) =1-P(0)-P(1)-P(2)-P(3)-P(4) =0.098