CH 6 - Normal Distribution.pdf - Chapter 6 6-1 Chapter 6...

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Chapter 6 6-1 ATW123 - Business Statistics [email protected] CH6 - 1 The Normal Distribution Chapter 6 CH6 - 2 Objectives In this chapter, you learn: To compute probabilities from the normal distribution How to use the normal distribution to solve business problems To use the normal probability plot to determine whether a set of data is approximately normally distributed CH6 - 3 Continuous Probability Distributions A continuous variable is a variable that can assume any value on a continuum (can assume an uncountable number of values) thickness of an item time required to complete a task temperature of a solution height, in inches These can potentially take on any value depending only on the ability to precisely and accurately measure CH6 - 4 Bell Shaped Symmetrical Mean, Median and Mode are Equal Location is determined by the mean, μ Spread is determined by the standard deviation, σ The random variable has an infinite theoretical range: + to   Mean = Median = Mode X f(X) μ σ The Normal Distribution CH6 - 5 The Normal Distribution Density Function 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 CH6 - 6 A B C A and B have the same mean but different standard deviations. B and C have different means and different standard deviations. By varying the parameters μ and σ, we obtain different normal distributions
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Chapter 6 6-2 ATW123 - Business Statistics [email protected] CH6 - 7 The Normal Distribution Shape X f(X) μ σ Changing μ shifts the distribution left or right. Changing σ increases or decreases the spread. CH6 - 8 The Standardized Normal Any normal distribution (with any mean and standard deviation combination) can be transformed into the standardized normal distribution (Z) To compute normal probabilities need to transform X units into Z units The standardized normal distribution (Z) has a mean of 0 and a standard deviation of 1 CH6 - 9 Translation to the Standardized Normal Distribution Translate from X to the standardized normal (the “Z” distribution) by subtracting the mean of X and dividing by its standard deviation: The Z distribution always has mean = 0 and standard deviation = 1 CH6 - 10 The Standardized Normal Probability Density Function 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 CH6 - 11 The Standardized Normal Distribution Also known as the “Z” distribution Mean is 0 Standard Deviation is 1 Z f(Z) 0 1 Values above the mean have positive Z-values.
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