Normal Distribution

Cards (14)

  • The normal distribution is for continuous variables
  • Normal Distribution: Y  N(μ, σ2)Y\ \sim\ N\left(\mu,\ \sigma^2\right)
  • Where are the points of inflection on the normal distribution?
    μ±σ\mu\pm\sigma
  • What percentage of data is within 2 σ\sigma of μ\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  N(0, 12)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 μ, σ\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:
    μ\mu = npnp
    σ\sigma = np(1 p)\sqrt{np\left(1-\ p\right)}
  • Continuity Correction: if approximating binomial as normal, change discrete values to continuous.

    P(X > 5)P\left(X\ >\ 5\right) = P(Y > 5.5)P\left(Y\ >\ 5.5\right)
    P(3 < X 11)P\left(3\ <\ X\ \le11\right) = P(3.5 < Y < 11.5)P\left(3.5\ <\ Y\ <\ 11.5\right)