Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

lauren_hicks

  • one year ago

In humans the intermidiate stage of sleep is characterized by the presence of high-amplitude waves averaging about 2 waves per second. Find the probability of observing 15 or more high-amplitude waves in a five-second period of intermediate sleep. Please help I'm pretty lost for some reason and I have to turn this in at 12:30

  • This Question is Open
  1. CarlosGP
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Too late for your assignment but on time to learn. Whenever you have a problem related to rates (such as the case of waves per second or calls per minute in a call center or fires per hour for a fire department and so on...) you need to apply Poisson Distribution. The formula is: \[P(X=k)=\lambda^ke^{-\lambda}/k!\]Lambda (λ) is the number of occurrences during the period of observation. In our case λ=(2 waves/second) x (5 seconds)=10 waves in 5 seconds as average rate. Your formula will be then: \[P(X=k)=10^ke^{-10}/k!\] The probability of observing less than 15 waves is the probability of observing up to 14 waves (in other words observing 0,1,2,3....14 waves). This can be expressed as:\[P(X < 15)=P(X \le 14)=\sum_{k=0}^{k=14}P(X=k)\] and the probability of observing 15 or more is\[P(X \ge 15)=1-P(X<15)=1-P(X \le 14)\] All this can be put as: \[P(X \ge 15)=1-\sum_{k=0}^{k=14}10^ke^{-10}/k!\] If you use Excel to calculate it, you get:\[P(X \ge 15)=1-0.9165=0.0835\] and that is the same than 8.35%

  2. Not the answer you are looking for?
    Search for more explanations.

    Search OpenStudy
    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.