Answered

Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Join our Q&A platform to get precise answers from experts in diverse fields and enhance your understanding. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

Among the most famous of all meteor showers are the Perseids, which occur each year in early August. In some areas the frequency of visible Perseids can be as high as 40 per hour. What is the probability that an observer who has just seen a meteor will have to wait at least 5 minutes before seen another.

Sagot :

nuhulawal20

Answer:

the required probability is 0.0357

Step-by-step explanation:

Given the data in the question;

X-Exp( λ = 40/60 = 0.6667

Pdf: f( x ) = λe^(-λx), 0 < x

so

Cdf: P( X < x ) = 1 - e^(-λe)

( X ≤ x ) = 1 - e^(-λe), for x > 0 ⇒ p( X > x ) = e^(-λe)

now to wait at least 5 minutes before seen another

p(X  > 5 ) = e^(-λe)

we substitute

p(X  > 5 ) = e^(-0.6667 × 5)

p(X  > 5 ) = e^(-3.3335)

p(X  > 5 ) = 0.035668 ≈ 0.0357

Therefore,  the required probability is 0.0357

Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.