Question

When a circuit board used in the manufacturing of compact disc players are tested. The long run percentage of defectives is 5% let x be the number of defective boards in a random sample of size n= 25, so X ~Bin(25,0.05)

Answer 1

Answer:

pts.) 3.48 (p.113). When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%. Let X = the number of defect boards in a random sample of size n = 25, so X ~ Bin(25, 0.05). a) Determine P(X 2) P(X 2) = P(X = 0) + P(X = 1) + P(X = 2) b) Determine P(X 5) P(X 5) = 1 –P(X 4) = 1 –[P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)] c) Determine P(1 X 4) P(1 X 4) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)] d) What is the probably that none of the 25 boards is defective? e) Calculate the expected value and standard deviation of X. E(X) = n ∙ p = 25 ∙ 0.05 = 1.25Var(X) = n ∙ p ∙ (1 –p) = 25 ∙ 0.05 ∙ 0.95 = 1.1875