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Chap 61 Statistics for Managers Using Microsoft174。 Excel 5th Edition Chapter 6 The Normal Distribution and Other Continuous Distributions Chap 62 Learning Objectives In this chapter, you will learn: ? To pute probabilities from the normal distribution. ? To use the normal probability plot to determine whether a set of data is approximately normally distributed. ? To pute probabilities from the uniform distribution. ? To pute probabilities from the exponential distribution Chap 63 Continuous Probability Distributions ? A continuous random 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 plete a task ? temperature of a solution ? height ? These can potentially take on any value, depending only on the ability to measure precisely and accurately. Chap 64 The Normal Distribution Properties ? ‘ Bell Shaped’ ? Symmetrical ? Mean, Median and Mode are equal ? Location is characterized by the mean, μ ? Spread is characterized by the standard deviation, σ ?The random variable has an infinite theoretical range: ? to +? Mean = Median = Mode f(X) μ σ Chap 65 The Normal Distribution Density Function 2μ)(X21e2 π1f ( X ) ?????? ??? ??? The formula for the normal probability density function is Where e = the mathematical constant approximated by π = the mathematical constant approximated by μ = the population mean σ = the population standard deviation X = any value of the continuous variable Chap 66 The Normal Distribution Shape By varying the parameters μ and σ, we obtain different normal distributions Chap 67 The Normal Distribution Shape X f(X) μ σ Changing μ shifts the distribution left or right. Changing σ increases or decreases the spread. Chap 68 The Standa