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?

Question

Ernie

Business

2 August, 13:26

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?

+4

Answers (1)

Know the Answer?

Paloma Boone · Answer 1

Consider the following calculations

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