Data gathered by the quality control department of a large manufacturing concern

Question

Data gathered by the quality control department of a large manufacturing concern led to the observation that the number of imperfections found on the plastic sheets used to produce industrial quality tarpaulin is a Poisson random variable with an average of 1.44 imperfections per 10 square meters.

a) What is the probability that more than 3 imperfections will be found in an area of 10 square meters?

b) Compute the probability that more than two but fewer than 6 imperfections will be found in an area of 20 square meters.

c) Compute the probability that at least 140 imperfections will be found in an area of 1,000 square meters.

Explanation / Answer

a) Excel function: =1 - POISSON.DIST(3,1.44,TRUE)
0.0583

1 - ke-/k! = 1 - 1.443*e-1.44/3! - 1.442*e-1.44/2! - 1.441*e-1.44/1! - 1.440*e-1.44/0!= 0.0583

b) =POISSON.DIST(5,2.88, TRUE) - POISSON.DIST(2,2.88,TRUE)
0.4771

2.883*e-2.88/3! + 2.884*e-2.88/4! + 2.885*e-2.88/5! = 0.4771

c) =1 - POISSON.DIST(139,144,TRUE)
0.6417

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.