Question

A pen company averages 1.2 defective pens per carton produced (200 pens). The number of defects per carton is Poisson distributed.

a. What is the probability of selecting a carton and finding two defective pens?



b. What is the probability of finding nine or more defective pens in a carton?



c. Suppose a purchaser of these pens will quit buying from the company if a carton contains more than three defective pens.




What is the probability that a carton contains more than three defective pens?

Answer 1

Consider the following calculations

Step-by-step explanation:

Using the following formulas we calculate the number of defects

a) P(x=2)=e^(-1.2)(1.2)^2/2!=0.217 [use e =2.718]

b) P(X>=9)=1-P(x<9)=1-0.9999=0.0001

P(x<9)=P(x=0)+...+P(x=8)

c) P(x>3)=1-P(x<=3)=1-0.966=0.034