Normal Distribution

A description of normal distribution

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Normal Distribution

  • Normal distribution is symmetrical about its mean (mean is in the center)
  • Has mode, median and mean which are all equal
  • Ranges from -infinity to infinity
  • Has a total area under the curve of unity
  • Has notation N(mean,varience), where the varience is the varience of the distribution

The standard normal distribution -

Any normal variable can be changed into a standard normal variable by using

(X - mean)/standard deviation

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Most questions will ask to find a probability that the normal distribution is less/more than a certain value

P(Z<1.69) - Find the value of 1.69 in the appendix, and the probability of 1.69 = 0.9545

P(Z< -2.18) - Find the value of 2.18 (because it is symmetrical, the negative sign does not change the value), then 1 - P(2.18) ... 1 - 0.9854 = 0.0146

P (-.131 < Z < 1.06) - Find the values of the probability of each of the numbers given by looking in the appendix

(0.8554 + 0.9049) - 1 = 0.7603

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