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  # Answer to Question #15911 in Statistics and Probability for lim
  
  Question #15911
  Find the indicated probability Weekly salaries of teachers in one state are normally distrubuted with a mean of \$490 and a standard deviation of \$45. What is the probblity that a randomly selected teacher earns more than \$525 a week?
  1
  2012-10-04T10:30:49-0400
  For any normal random variable X with mean μ and standard deviation σ , X ~
  Normal( μ , σ ), (note that in most textbooks and literature the notation is
  with the variance, i.e., X ~ Normal( μ , σ² ). Most software denotes the normal
  with just the standard deviation.)
  
  You can translate into standard normal
  units by:
  Z = ( X - μ ) / σ
  
  Moving from the standard normal back to
  the original distribuiton using:
  X = μ + Z * σ
  
  Where Z ~ Normal( μ =
  0, σ = 1). You can then use the standard normal cdf tables to get
  probabilities.
  
  If you are looking at the mean of a sample, then remember
  that for any sample with a large enough sample size the mean will be normally
  distributed. This is called the Central Limit Theorem.
  
  If a sample of
  size is is drawn from a population with mean μ and standard deviation σ then the
  sample average xBar is normally distributed
  
  with mean μ and standard
  deviation σ /√(n)
  
  In this question we have
  X ~ Normal( μx = 490 , σx²
  = 2025 )
  X ~ Normal( μx = 490 , σx = 45 )
  
  Find P( X > 525 )
  P(
  ( X - μ ) / σ > ( 525 - 490 ) / 45 )
  = P( Z > 0.7777778 )
  = P( Z
  < -0.7777778 )
  = 0.21835
  
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