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Formula Review

7.1 The Central Limit Theorem for Sample Means (Averages)

Central limit theorem for sample means: X ¯ X ¯ ~ N ( μ x ,  σx n ) ( μ x ,  σx n )

Mean X ¯ X ¯ : μx

Central limit theorem for sample means z-score and standard error of the mean: z= x ¯ − μ x ( σ x n ) z= x ¯ − μ x ( σ x n )

Standard error of the mean (standard deviation ( X ¯ X ¯ )): σ x n σ x n

7.2 The Central Limit Theorem for Sums (Optional)

Central limit theorem for sums: ∑X ~ N[(n)(μx),( n n )(σx)]


 

Mean for sums (∑X): (n)(μx)


 

Central limit theorem for sums z-score and standard deviation for sums: z  for the sample mean =  Σx–(n)( μ X ) ( n )( σ X ) z for the sample mean =  Σx–(n)( μ X ) ( n )( σ X )


 

Standard deviation for sums (∑X): ( n ) ( n ) (σx)