Chapter6,NormalDistribution.pptVIP

Ch. 6 The Normal Distribution 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 complete a task temperature of a solution height, in inches These can potentially take on any value, depending only on the ability to measure accurately. The polygon of the distribution become a smooth curve called Probability Density Function (this is equivalent to Probability Distribution for discrete random variable) The Normal Distribution Bell Shaped Perfectly Symmetrical Mean, Median and Mode are Equal Location on the value axis is determined by the mean, μ Spread is determined by the standard deviation, σ The random variable has an infinite theoretical range: + ? to ? ? What can we say about the distribution of values around the mean? There are some general rules: Probability is measured by the area under the curve The total area under the curve is 1.0, and the curve is symmetric, so half is above the mean, half is below The height of the curve at a certain value below the mean is equal to the height of the curve at the same value above the mean The area between: The Normal Distribution Density Function: The formula for the normal probability density function is: (the curve is generated by): By varying the parameters μ and σ, we obtain different normal distributions. That is to say that any particular combination of μ and σ, will produce a different normal distribution. This means that we have to deal with numerous distribution tables. Standard Normal Distribution Any normal distribution (with any mean and standard deviation combination) can be transformed into the standardized normal distribution (Z). To do so, we need to transform all X units (values) into Z units (values) Then the resulting standard normal distribution has a mean=zero and a standard deviation =1 X-Values above the mean of X will have positive Z-value and X-values be