Normal Distbns

# Normal Distbns - Normal Distributions and Uniform...

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Normal Distributions and Uniform Distributions © 2010 Radha Bose FSU Department of Statistics 1 Additional items: How to use the z-table pp.1-4, z-table. DENSITY CURVE ~ smooth curve that models the general shape of a distribution, ignoring irregularities or outliers ~ curve shows what distribution looks like after very many observations are taken, thus it is a model for the population ~ Greek letters generally used to represent population parameters associated with density curves ~ horizontal axis is data axis ~ curve always runs on or above horizontal axis any curve that satisfies these two properties ~ total area under curve is 1 can be used to model data ~ area under curve represents percentage of data: area under curve above an interval of values = proportion of data in that interval ~ curve is used to find proportion of data within a certain interval of values ~ the proportion of data equal to a single value is considered to be zero ~ in a symmetric density curve, mean = median ~ in a left-skewed density curve, mean < median ~ in a right-skewed density curve, mean > median

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Normal Distributions and Uniform Distributions © 2010 Radha Bose FSU Department of Statistics 2 THE CONTINUOUS UNIFORM DISTRIBUTIONS ( ) , U α β ~ data values range from lower limit α to upper limit β , inclusive ~ model characterized by parameters α and β ~ density curves are horizontal straight lines that run strictly above the horizontal axis ~ area under curve is rectangular in shape and total area is 1 , so we necessarily have 1 Height β α = - ~ areas under curve obtained by using Height Length Area × = 1. The ages of the children who have attended and who are currently attending a certain daycare facility are evenly distributed between 3 years and 8 years. Their ages therefore follow a U(3,8) years distribution, which is shown below. 3 8 Age (years) (a) What is the total area under the curve? ______________________________ What is the length of the curve? ______________________________ So now, what is the height of the curve? ______________________________
Normal Distributions and Uniform Distributions © 2010 Radha Bose FSU Department of Statistics 3 (b) What is the median age? ______________________________ So now, what is the mean age ______________________________ (c) What are the quartiles of the distribution? ______________________________ So now, what is the interquartile range of the distribution?

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