Answer to Question #170299 in Statistics and Probability for Bikram Chaudhary

Question

If the chance of being defective bottles of medicine produced by a manufacturer is 1/1000. the bottles are packed in boxes containing 500 bottles. A drug manufacturer buys 100 boxes from the producer of bottles. Find how many boxes contain i) no defectives (ii) less than 2 defectives bottle.

Answer 1

$λ = 0.001 \times 500 = 0.5$

i) $P(X=0) = e^{-0.5} \times \frac{0.5^0}{0!} = e^{-0.5} = 0.606$

$N = 100 \times 0.606 = 60.6 ≈ 61$

ii) $P(X<2) = P(X=0) + P(X=1) + P(X=2)$

$P(X=1) = e^{-0.5} \times \frac{0.5^1}{1!} = 0.5e^{-0.5} \\ P(X=2) = e^{-0.5} \times \frac{0.5^2}{2!} = 0.125e^{-0.5} \\ P(X<2) = e^{-0.5} + 0.5e^{-0.5} + 0.125e^{-0.5} = 1.625e^{-0.5} = 0.9856 \\ N = 100(1 -0.9856) = 1.44 ≈ 2$