The Normal Distribution Density Function The formula for the normal probability density function is X)22o Where e=the mathematical constant approximated by 2.71828 =the mathematical constant approximated by 3.14159 u=the population mean o=the population standard deviation X=any value of the continuous variable,R.V. Statistics for Managers Using Microsoft Excel Chap 6-11
Statistics for Managers Using Microsoft Excel Chap 6-11 The Normal Distribution Density Function 2 (X μ ) 2 1 e 2 π 1 f(X) The formula for the normal probability density function is Where e = the mathematical constant approximated by 2.71828 π = the mathematical constant approximated by 3.14159 μ = the population mean σ = the population standard deviation X = any value of the continuous variable, R.V
The Standardized Normal Distribution Any normal distribution(with any mean and standard deviation combination)can be transformed into the standardized normal distribution(Z)☑. Need to transform X units into Z units Statistics for Managers Using Microsoft Excel Chap 6-12
Statistics for Managers Using Microsoft Excel Chap 6-12 The Standardized Normal Distribution Any normal distribution (with any mean and standard deviation combination) can be transformed into the standardized normal distribution (Z). Need to transform X units into Z units
The Standardized Normal Distribution Translate from X to the standardized normal (the "Z"distribution)by subtracting the population mean of X and dividing by its standard deviation (Transformation Formula ) Z= X-4 Z always has mean =0 and standard deviation Statistics for Managers Using Microsoft Excel Chap 6-13
Statistics for Managers Using Microsoft Excel Chap 6-13 The Standardized Normal Distribution σ X μ Z Translate from X to the standardized normal (the “Z” distribution) by subtracting the population mean of X and dividing by its standard deviation (Transformation Formula ): Z always has mean = 0 and standard deviation = 1
The Standardized Normal Distribution:Density Function The formula for the standardized normal probability density function is f(Z)= e 2 √2元 Where e=the mathematical constant approximated by 2.71828 =the mathematical constant approximated by 3.14159 Z=any value of the standardized normal distribution Statistics for Ma nagers Using Microsoft Excel Chap 6-14
Statistics for Managers Using Microsoft Excel Chap 6-14 The Standardized Normal Distribution: Density Function 2 Z 2 e 2 π 1 f(Z) The formula for the standardized normal probability density function is Where e = the mathematical constant approximated by 2.71828 π = the mathematical constant approximated by 3.14159 Z = any value of the standardized normal distribution
The Standardized Normal Distribution:Shape Also known as the“Z”distribution > Mean is 0 >Standard Deviation is 1 fZ☑ 0 Values above the mean have positive Z-values, Values below the mean have negative Z-values Statistics for Managers Using Microsoft Excel Chap 6-15
Statistics for Managers Using Microsoft Excel Chap 6-15 The Standardized Normal Distribution: Shape Z f(Z) 0 1 Also known as the “Z” distribution Mean is 0 Standard Deviation is 1 Values above the mean have positive Z-values, Values below the mean have negative Z-values