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Section 5.1 ~ What is Normal? Introduction to Probability and Statistics Ms. Young ~ room 113 Sec. 5.1 Objective In this section you will understand what is meant by a normal distribution and be able to identify situations in which a normal distribution is likely to arise. Sec. 5.1 Normal Distribution A normal distribution has the following characteristics: Single-peaked Symmetric (mean and median are the same as the mode) The curve is spread out in the shape of a bell (“bell-shaped” distribution) Sec. 5.1 Normal Distribution Cont’d… All normal distributions have the same characteristic bell shape, but can differ in their mean and variation Knowing the mean and the standard deviation of a normal distribution tells you everything you need to know about its variation The following distributions have the same mean, but different standard deviations Sec. 5.1 The Normal Distribution and Relative Frequencies The area that lies under the curve corresponding to a range of values on the x-axis is the relative frequency of those values The total area under the curve is 1, or 100% because the total relative frequency for the histogram is 1 or 100% Sec. 5.1 When Can We Expect a Normal Distribution? Here are some common circumstances in which you can expect a normal distribution to occur: Physical characteristics such as: Standardized test scores such as: Height, weight, blood pressure, & reflex times SAT’s, IQ tests, PSSA’s, etc. Sports statistics such as: Batting averages, times in swimming, results in a track meet, etc. Sec. 5.1 Summary A distribution is likely to be normal if it satisfies the following criteria: Most data values are clustered near the mean, giving the distribution a well defined single peak Data values are spread evenly around the mean, making the distribution symmetric Larger deviations from the mean become increasingly rare, producing tapering tails of the distribution (therefore creating the bell shape) Individual data values result from a combination of many different factors, such as genetic and environmental factors