Question

A computer manufacturing company produce chips with defect probability 0.001. In a package of 2000 chips, denote the number of defective chips by X. Use Poisson distribution for approximation: The Poisson parameter for X is: , P(X 3) =?

Answer 1

Ans:

Poisson approximation:

Poisson parameter for X:

$\lambda =np=0.001*2000=2$

P(X>1)=1-P(x=0)-P(x=1)

=1-e^-2*(2⁰/0!)-e^-2*(2¹/1!)

=1-e^-2*(1+2)=0.5940

P(X<=3)=P(x=0)+P(x=1)+P(x=2)+P(x=3)

=e^-2*(2⁰/0!)+e^-2*(2¹/1!)+e^-2*(2²/2!)+e^-2*(2³/3!)

=e^-2*(1+2+2+1.333)

=e^-2*6.333=0.8571