Question

3. A factory produces screws in batches of 100,000. The probability that a screw is defective is 0.01%. Assume that defects occur independently of each other.

(a) Approximate the probability that 15 or more screws in a batch are defective using the normal approximation to the binomial distribution.

(b) Approximate the probability that 3 or fewer screws in a batch are defective using the normal approximation to the binomial distribution.

(c) Approximate the probability that 3 or fewer screws in a batch are defective using the Poisson approximation to the binomial distribution.

Answer 1

3.162 a) p = 0.0001; n = 109; X ~ Bin (10%, 0.0001); Normal approx, X - Normallu = np= 10, o = 3.162); 15 - 10 P(X > 15) = P(Z > =) = P(Z > 1.58) = 0.057 6) P(X < 3) = P(Z <-9765) = P(Z < -2.213) = 0.013 c) Poisson approximation : X = np = 10; P(X < 3) = [ 1019 = 0.01034 1 k= 0