text: Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °
  
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  ## #1 2013-04-23 21:27:44
  
  MathNewbie22
  Novice
  
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  ### Probability
  
  A set of final exam marks in a stats course is normally distributed, with a mean of 73 and a standard deviation of 9.
  What is the probability that a student scored below 85 on this exam? Round to 4 decimal places as needed.
  
  I don't understand this question either. Any help would be much appreciated ~~"..
  
  ## #2 2013-04-23 23:07:25
  
  bob bundy
  Moderator
  
  Offline
  
  ### Re: Probability
  
  hi MathNewbie22,
  
  Take a look at
  
  http://www.mathsisfun.com/data/standard … table.html
  
  This normal graph is brilliantly interactive.  You slide the z value about and it gives you the probability as a percentage.
  
  For your question you need to choose the display option 'up to z'
  
  Now to decide what z is for your question.
  
  Clearly, you couldn't have a separate graph for every possible mean and every possible standard deviation.  You'd need an infinite number of them!!!
  
  So statisticians have just one, the standard normal graph, which has a mean of zero and a sd. of 1.
  
  So you have to convert your question into the standard graph version.
  
  The score is 85 so it is 85 - 73 from the mean.
  
  So imagine the whole graph shifted 73 places left.  Now the mean is at zero and your 85 has become 12
  
  So the equivalent question would be a mean of zero and a score of 12.
  
  But the sd. is also wrong.  The graph needs rescaling so that it has a sd. of 1.
  
  You do that by dividing by 9.
  
  Thus mean 73, sd 9 and score 85 becomes mean 0, sd. 1 and score
  
  On the graph move the sllder until you get this z value and there's the probability.
  
  In an exam they won't let you carry a computer in and go on-line, so how do you do the question then?
  
  Look below the graph and you'll find a table of probabilities for given z values.
  
  This table starts at the half way value of z = 0 and goes up to a z value of 3.09.  It saves space by not giving the other half of the table, which would be the same by symmetry.
  
  So you look for your z value, read off the probability, and add 0.5 for the missing half of the table.
  
  Bob
  
  You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
explanation: The text extract is a forum post from a math discussion board. It contains a math question about probability and a detailed response providing a solution. The question asks for the probability that a student scored below 85 on a normally distributed exam with a mean of 73 and a standard deviation of 9. The response explains how to use a standard normal distribution table to find the probability.
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: Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °
  
  You are not logged in.
  
  ## #1 2013-04-23 21:27:44
  
  MathNewbie22
  Novice
  
  Offline
  
  ### Probability
  
  A set of final exam marks in a stats course is normally distributed, with a mean of 73 and a standard deviation of 9.
  What is the probability that a student scored below 85 on this exam? Round to 4 decimal places as needed.
  
  I don't understand this question either. Any help would be much appreciated ~~"..
  
  ## #2 2013-04-23 23:07:25
  
  bob bundy
  Moderator
  
  Offline
  
  ### Re: Probability
  
  hi MathNewbie22,
  
  Take a look at
  
  http://www.mathsisfun.com/data/standard … table.html
  
  This normal graph is brilliantly interactive.  You slide the z value about and it gives you the probability as a percentage.
  
  For your question you need to choose the display option 'up to z'
  
  Now to decide what z is for your question.
  
  Clearly, you couldn't have a separate graph for every possible mean and every possible standard deviation.  You'd need an infinite number of them!!!
  
  So statisticians have just one, the standard normal graph, which has a mean of zero and a sd. of 1.
  
  So you have to convert your question into the standard graph version.
  
  The score is 85 so it is 85 - 73 from the mean.
  
  So imagine the whole graph shifted 73 places left.  Now the mean is at zero and your 85 has become 12
  
  So the equivalent question would be a mean of zero and a score of 12.
  
  But the sd. is also wrong.  The graph needs rescaling so that it has a sd. of 1.
  
  You do that by dividing by 9.
  
  Thus mean 73, sd 9 and score 85 becomes mean 0, sd. 1 and score
  
  On the graph move the sllder until you get this z value and there's the probability.
  
  In an exam they won't let you carry a computer in and go on-line, so how do you do the question then?
  
  Look below the graph and you'll find a table of probabilities for given z values.
  
  This table starts at the half way value of z = 0 and goes up to a z value of 3.09.  It saves space by not giving the other half of the table, which would be the same by symmetry.
  
  So you look for your z value, read off the probability, and add 0.5 for the missing half of the table.
  
  Bob
  
  You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The text extract is a forum post from a math discussion board. It contains a math question about probability and a detailed response providing a solution. The question asks for the probability that a student scored below 85 on a normally distributed exam with a mean of 73 and a standard deviation of 9. The response explains how to use a standard normal distribution table to find the probability.
  
  Label: question-and-answer