Normal Distribution: Bell Curve

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Last updated 4:52 AM on 4/11/26
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6 Terms

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Normal Distribution: Bell Curve Distribution (Normally Distributed Variable)

When the mode, mean and median are roughly the same. (50% more and 50% less)

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The Empirical Rule(s)

3 and can only be applied to a bell curve (normally distributed variable). YOU MUST BE EXPLICITLY TOLD THERE IS A BELL CURVE TO SOLVE USING THESE RULES, IF NOT, YOU CANNOT SOLVE.

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1 SD

68%

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2 SD

95%

5
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3 SD

99.7%

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Examples

EX 1: mean is 120. 1 SD = 20 points. What % of the observations are between 100 and 140? Supposed the sample size is 500.

Answer: 100-140 are between 68% (1 SD).

EX 2: How many observations are between 100-140? .68 × 500 = 340.

EX 3: Quantify 145: 100 - 68 = 32 (half and half: bell curve). 32/2 = top 16%

EX 4: 165? 100 - 95 = 5. 5/2 = top 2.5%