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 no defective pens? b. What is the probability of finding eight 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 five defective pens. What is the probability that a carton contains more than five defective pens? P(x = 0 | λ = 1.2) = b. P(x ≥ 8 | λ = 1.2) = c. P(x > 5 | λ = 1.2) =

a. P(x = 0 | λ = 1.2) = 0.301

b. P(x ≥ 8 | λ = 1.2) = 0.000

c. P(x > 5 | λ = 1.2) = 0.002

Step-by-step explanation:

If the number of defects per carton is Poisson distributed, with parameter 1.2 pens/carton, we can model the probability of k defects as:

a. What is the probability of selecting a carton and finding no defective pens?

This happens for k=0, so the probability is:

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

This can be calculated as one minus the probablity of having 7 or less defective pens.

c. Suppose a purchaser of these pens will quit buying from the company if a carton contains more than five defective pens. What is the probability that a carton contains more than five defective pens?

We can calculate this as we did the previous question, but for k=5.