Normal Distribution

• The normal distribution is for continuous variables
• Normal Distribution: $Y\ \sim\ N\left(\mu,\ \sigma^2\right)$
• Where are the points of inflection on the normal distribution?

  $\mu\pm\sigma$
• What percentage of data is within 2 $\sigma$ of $\mu$ ?


  95%
• How many standard deviations away from the mean contains 99.7% of the population?

  3
• To find the probabilities and the inverse normal, you need to use your calculator
• Standard Normal Distribution:

  $Z\ \sim\ N\left(0,\ 1^2\right)$
• What letter do we use for the Normal Distribution?

  Y
• What letter do we use for the Standard Normal Distribution?

  Z
• If you are missing $\mu,\ \sigma$ or both:


  Use coding, or simultaneous equations for both
• What does n have to be to approximate binomial distributions as normal distributions?

  large
• What does p have to be to approximate binomial distributions as normal?

  approximately 0.5
• To approximate a binomial as normal:

  $\mu$ = $np$

  $\sigma$ = $\sqrt{np\left(1-\ p\right)}$
• Continuity Correction: if approximating binomial as normal, change discrete values to continuous.

  
  

  $P\left(X\ >\ 5\right)$ = $P\left(Y\ >\ 5.5\right)$

  $P\left(3\ <\ X\ \le11\right)$ = $P\left(3.5\ <\ Y\ <\ 11.5\right)$