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More on Normal Distributions


  1. 68% of the distribution is within one standard deviation of the mean. 40 + 5 = 45, 40 - 5 = 35

  2. 95% of the distribution is within 1.96 standard deviations of the mean. You can round 1.96 to 2 to approximate. 20 - 2(3) = 14, 20 + 2(3) = 26

  3. Use the "Calculate Area for a given X" calculator and enter Mean = 5, SD = 2, Above 3. You will get 0.8413.

  4. Var = 100, so SD = 10. Use the "Calculate X for a given Area" calculator and enter Mean = 120, SD = 10, Shaded area = .35. Click below, and you will get 116.15.

  5. Use the "Calculate X for a given Area" calculator and enter Mean = 38, SD = 6, Shaded area = .80. Click below, and you will get 43.05, meaning a score of 43.

  6. Use the "Calculate Area for a given X" calculator and enter Mean = 38, SD = 6, Between 30 and 45. You will get 0.787, meaning 78.7%.