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Y R 4 - NN (1= 0 T 77 B iy Norm (arca fo A lef) M,&’) Standard Normal e iV\V/\)DYM(.O—Z,S) /20/ 7>';5b.w Standardizing is a technique to help us determine percentages, proportions, probabilities, or area under the curve for any set of data. The new values are unit-less. The requirement is that the data must be normally or approximately T T TR — normally distributed. We will use TABLE Z from your text. d o ils Q[ . Standarel Mg, Finding Normal Percentiles using Table Z: /tL '-——'O iy T ‘ Example #1: Use the Z table to find the following: Draw the picture first, shade the region you want and look up the Z in Table & to find the proportion to the left of that z-score. The proportion is also known as probability that the value of a particular member of a population will fall in the given interval. a. P(Z<-1.42)= .077 & b. P(Z>195)= C. ‘ NOC \C_O\‘F =] .82 -\.02 © 257 U\ ) ( sl Example #2: Women's heights Assume that college women'’s heights follow a normal curve with rghtof 65 inchesand a standard o= | Find the probability a college woman, selected at random, is shorter thm@nches? /“\ ITt=») (\ormod\co\{:(\ow,\’\" \n, M, 00 P(X & (o?/%: (—-qq qqqq) @Z/QS) Z’?) b o (OZ‘{aS_ ] ANJTwensS \ 8 : 2 & \ae\g}\/bd‘» IS 2 b) Find the probability a college woman, selected at random, is more than 68 inches tall? nomadcd S (R,000099 4527 ) . = 1233 * I Tk g ¢) Find the probability a college woman, selected at random, is between 60 and 68 inches tall? P'D\OQ y r\orm%iiG (0,08 65, 2,7 . A 0 \ \ Ww 65 Y