Question

Historical data for a local steel manufacturing company shows that the average number of defects per standard sheet of steel is 2. In addition, the number of defects per unit is distributed according to Poisson distribution.
1. A batch has just been completed. What is the probability that the first three units manufactured in this batch will contain at least a total of 4 defects?
A.8488 B.7149 C.1512 D.2851

Answer 1

Answer:

Therefore the correct answer is A.) 84.88%

Step-by-step explanation:

i) λ = 2

ii) λ for three units = 2 $\times$ 3 = 6

iii) P(x ≥ 4) = 1 - P(x < 4) = 1 - {P(x = 0) + P(x = 1) + P(x = 2)  + P(x = 3) }

                                = 1 - { $\frac{e^{-6}6^{0} }{ 0!} + \frac{e^{-6}6^{1} }{ 1!} + \frac{e^{-6}6^{2} }{ 2!} + \frac{e^{-6}6^{3} }{ 3!}$  }

                                = 1 - (0.0025 + 0.0149 + 0.0446 + 0.0892)

                                = 0.8488

 Therefore the correct answer is A.) 84.88%