Question

EVGA Corporation is a computer hardware company that produces Nvidia-GPU- based video cards as well as Intel-chipset-based motherboards. Suposse that their products are independently defective with probability 0.006. (a) (12.5 points) Find the probability that a sample of 70 items will contain at least 2 defective items (b) (12.5 points) Find the Poisson approximation for the probabilily in (a)

Answer 1

no soli let je denohe the items with $= 0.006 then Xu B (m, 0.006). then prob. of defective n-2 p(X=x) = n q X x=0, 1, 2,.. ($+q) = 1. Now (a) Here na to, p= 0.006,9=1-6 qol-0.006 =0.994. Prob. of containing at least a defective items in a sample of Heme P (X2) la P(X22) 1-PCX=o) + P(X=1) 1-P(X=0) + P(x = 1)] 170 (0.006 0.94 69 +70 (0.006) (994)

10 697 691 P(X),2) - la 1- [1(1)(0.994) #670)(0.008)(0.my) 1-60.494) +40)(0.006)(0.994) 0.656214(0.42)(0.66017 -|- [0.65621 +0.27727] =) - 0.93348 0.06652 P(X72) 0.06652 Are (6) For a= np (0) (0.006) = 0.42 Thus the poission approximation for the Probability P(X3, 2) is PLX>,2) I-P(X<2) 1-(P(X=0) + + P(x=1) 10:42) 20.42 (0.42) -0.42 = + -0.42 - Oolta lale +0.42 e 10.65704 +0.27595] 10.93299 =10.obtoll Ans P(x>2)