text: # Gaussian Distribution
  
  • Apr 17th 2007, 03:09 PM
  thefirsthokage
  Gaussian Distribution
  The strength levels of a group of Martians follows Normal distribution with a mean of 75kgf and a std. dev. of 5kgf.
  
  (a) How many Martians do you expect to meet before you find one with a strength level greater than 72 kgf?
  
  (b) In a group of 5 Martians, what is the probability that exactly 4 Martians have strength levels greater than 72 kgf?
  
  (c) 4 Martians are trying to open a huge stone door which will open only if all of their individual strength levels are greater than 72 kgf. What is the probability that they will open the door?
  
  EDIT: Never mind I figured out (a) and (c). Still need help on (b), though. Thanks. I'll probably kick myself for not seeing it, but oh well.
  • Apr 27th 2007, 12:42 PM
  CaptainBlack
  Quote:
  
  Originally Posted by thefirsthokage
  The strength levels of a group of Martians follows Normal distribution with a mean of 75kgf and a std. dev. of 5kgf.
  
  (a) How many Martians do you expect to meet before you find one with a strength level greater than 72 kgf?
  
  (b) In a group of 5 Martians, what is the probability that exactly 4 Martians have strength levels greater than 72 kgf?
  
  (c) 4 Martians are trying to open a huge stone door which will open only if all of their individual strength levels are greater than 72 kgf. What is the probability that they will open the door?
  
  EDIT: Never mind I figured out (a) and (c). Still need help on (b), though. Thanks. I'll probably kick myself for not seeing it, but oh well.
  
  Calculate the probability p(72) that a martian has strength > 72 kgf. Then
  the number with strength >72 kgf in a sample of 5 has a binomial distribution
  B(p(72), 5). So prob of 4 having strength >72 kgf is b(4, p(72), 5).
  
  RonL
explanation: The text extract is a forum post discussing a problem related to the Gaussian (Normal) distribution of Martian strength levels. The post contains multiple questions (a, b, c) and an edit indicating that the author has figured out parts (a) and (c) but still needs help with part (b). The post also includes an answer provided by another user (CaptainBlack) for part (b).
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # Gaussian Distribution
  
  • Apr 17th 2007, 03:09 PM
  thefirsthokage
  Gaussian Distribution
  The strength levels of a group of Martians follows Normal distribution with a mean of 75kgf and a std. dev. of 5kgf.
  
  (a) How many Martians do you expect to meet before you find one with a strength level greater than 72 kgf?
  
  (b) In a group of 5 Martians, what is the probability that exactly 4 Martians have strength levels greater than 72 kgf?
  
  (c) 4 Martians are trying to open a huge stone door which will open only if all of their individual strength levels are greater than 72 kgf. What is the probability that they will open the door?
  
  EDIT: Never mind I figured out (a) and (c). Still need help on (b), though. Thanks. I'll probably kick myself for not seeing it, but oh well.
  • Apr 27th 2007, 12:42 PM
  CaptainBlack
  Quote:
  
  Originally Posted by thefirsthokage
  The strength levels of a group of Martians follows Normal distribution with a mean of 75kgf and a std. dev. of 5kgf.
  
  (a) How many Martians do you expect to meet before you find one with a strength level greater than 72 kgf?
  
  (b) In a group of 5 Martians, what is the probability that exactly 4 Martians have strength levels greater than 72 kgf?
  
  (c) 4 Martians are trying to open a huge stone door which will open only if all of their individual strength levels are greater than 72 kgf. What is the probability that they will open the door?
  
  EDIT: Never mind I figured out (a) and (c). Still need help on (b), though. Thanks. I'll probably kick myself for not seeing it, but oh well.
  
  Calculate the probability p(72) that a martian has strength > 72 kgf. Then
  the number with strength >72 kgf in a sample of 5 has a binomial distribution
  B(p(72), 5). So prob of 4 having strength >72 kgf is b(4, p(72), 5).
  
  RonL
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The text extract is a forum post discussing a problem related to the Gaussian (Normal) distribution of Martian strength levels. The post contains multiple questions (a, b, c) and an edit indicating that the author has figured out parts (a) and (c) but still needs help with part (b). The post also includes an answer provided by another user (CaptainBlack) for part (b).
  
  Label: multiple-question-and-answer