Answered

Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Get quick and reliable solutions to your questions from a community of experienced experts on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Contamination is a problem in the manufacture of optical storage disks. The number of particles of contamination that occur on an optical disk has a Poisson distribution, and the average number of particles per square centimeter of media surface is 0.1. The area of a disk under study is 100 cm2. Find the probability more than 12 particles occur in the area of a disk under study.

Sagot :

anuksha0456

The probability that more than 12 particles occur in the area of a disk under the study is 0.20844.

The number of particles follows a Poisson Distribution.

A Poisson Distribution over a variable X, having a mean λ, has a probability for a random variable x as  [tex]P(X = x) = e^{-\lambda} \frac{\lambda^{x}}{x!}[/tex] .

In the question, x = 12.

λ = 100*0.1 = 10.

To find : P(X > 12)

P(X > 12) = 1 - P(X ≤ 12) = 1 - poissoncdf(10,12)

As to find the probability of a Poisson Distribution P(X ≤ x), for a mean = λ, we use the calculator function poissoncdf(λ,x).

Therefore, P(X > 12) = 1 - 0.79156 = 0.20844.

Therefore, the probability that more than 12 particles occur in the area of a disk under the study is 0.20844.

Learn more about the Poisson Distribution at

https://brainly.com/question/7879375

#SPJ4

Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.