Question

Question 30 1 pts A manufacturer of processing chips knows that two percent of its chips are defective in some way. Suppose an inspector randomly selects four chips for an inspection. (a) Find the probability that a randomly selected chip is NOT defective. (b) Find the probability that all four chips are NOT defective. (c) Find the probability that at least one of the selected chips is defective. (Round your answer to three decimal places).

Answer 1

Solution: Probability that a chip is defective = p = 2% = 0.02 Probability that a chip is not defective = q = 1 – 0.02 = 0.98 Sample size = n = 4 Part-A: Probability that a randomly selected chip is not defective = 0.98 Part-B: Probability that all 4 chips are not defective = P(x = 4) Using Binomial distribution: P(x = 4) = f(4) =4Ca x (0.98)4 x (1 – 0.98)4-4 = 0.922 Therefore, probability that all 4 chips are not defective = 0.922 Part-C: Probability that at least one of the selected chips is defective = P(x > 1) P(x > 1) = 1 - P(x = 0) Using Binomial distribution: P(x = 0) = f(0) =“Cox (0.02)ºx (1 – 0.02)4–0 = 0.9224 = Hence, P(x > 1) = 1 – 0.9224 = 0.078 Therefore, probability that at least one of the selected chips is defective = 0.078