Normal distribution and continuous random variable

Lessons

• Introduction
  
  $\cdot$ Why are z-scores needed for random continuous variables?
  $\cdot$ Relationship between area under the curve and probability
  $\cdot$ Leads to Standard normal distribution
  

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• 1.
  Reading the Z Table
  Use the Z table to find:
  
  a)

  the z-score when the area under the curve to the left of z is 0.3015.
  
  
  b)

  the area from the mean to a z-score of 1.45.
  
  
  c)

  the z-score when the area under the curve to the left of z is 0.7774.
  
  

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• 2.
  Finding Probabilities from Z-Scores
  Answer the following questions based on the properties of standard normal distribution.
  
  a)

  What is the probability of having a z-score that is less than 0.75?
  
  
  b)

  What is the probability of having a z-score that is greater than -1.83?
  
  
  c)

  What is the probability of having a z-score that is between -1.27 to 1.06?
  
  

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• 3.
  Finding Z-Scores from Areas
  Answer the following questions based on the properties of standard normal distribution.
  i) by Z table
  ii) by calculator
  
  a)

  Find the z-score that represents the bottom 70%.
  
  
  b)

  Find the z-score that represent the top 70%.
  
  
  c)

  Find the z-scores that represent the top 4% and the bottom 4%.
  
  

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