Formula Review

7.1 The Central Limit Theorem for Sample Means (Averages)

Central limit theorem for sample means: X¯X¯ ~ N(μxσxn)(μxσxn)

Mean X¯X¯: μx

Central limit theorem for sample means z-score and standard error of the mean: z=x¯μx(σxn)z=x¯μx(σxn)

Standard error of the mean (standard deviation (X¯X¯)): σxnσxn

7.2 The Central Limit Theorem for Sums (Optional)

Central limit theorem for sums: ∑X ~ N[(n)(μx),(nn)(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)(μX)(n)(σX)z for the sample mean = Σx(n)(μX)(n)(σX)


 

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