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0 180 190 200 210 5 4 3 2 1 High dispersion Value on Variable Average Deviation 0)(?? ?nXX iCopyright 169。 2022 by Harcourt, Inc. All rights reserved. Copyright 169。 2022 by Harcourt, Inc. All rights reserved. Normal Distribution MEAN Copyright 169。 2022 by Harcourt, Inc. All rights reserved. Standard Normal Curve ? The curve is bellshaped or symmetrical ? About 68% of the observations will fall within 1 standard deviation of the mean ? About 95% of the observations will fall within approximately 2 () standard deviations of the mean ? Almost all of the observations will fall within 3 standard deviations of the mean Copyright 169。 2022 by Harcourt, Inc. All rights reserved. Standardized Values ? Used to pare an individual value to the population mean in units of the standard deviation ????xzLinear Transformation of Any Normal Variable into a Standardized Normal Variable 2 1 0 1 2 Sometimes the scale is stretched Sometimes the scale is shrunk ????????X ???? xzCopyright 169。 2022 by Harcourt, Inc. All rights reserved. Sample Distribution _ C? X S Copyright 169。 2022 by Harcourt, Inc. All rights reserved. Copyright 169。 2022 by Harcourt, Inc. All rights reserved. XclSZ? ECopyright 169。 2022 by Harcourt, Inc. All rights reserved. Copyright 169。 2022 by Harcourt, Inc. All rights reserved. Sample Size Formula example Suppose a survey researcher, studying expenditures on lipstick, wishes to have a 95 percent confident level (Z) and a range of error (E) of less than $. The estimate of the standard deviation is $. Copyright 169。 2022 by Harcourt, Inc. All rights reserved. 99% Confidence Calculating Sample Size [? ]?1389 ??265 . 37 2 ??2 53 . 74 2 ??????????????2 ) 29 )( 57 . 2 ( n 2 ??????????????]?347 ??[? 6325 . 18 2 ??4 53 . 74 2 ??????????????4 ) 29 )( 57 . 2 ( n 2 ??????????????Copyright 169。 2022 by Harcourt, Inc. All rights reserved.