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AP Statistics: Section 2.2 B Recall finding a z-score in section 2.1: X z = ------------. We can use this formula to take any particular observation in a Normal distribution and convert it to a z-score. This new distribution of z-scores is called the standard Normal distribution ____________________________. Its mean will be _____ 0 and its standard deviation will be _____. 1 The notation for the standard Normal distribution is ______. N (0,1) The standard Normal distribution is a density curve and thus the area under the curve must equal ____ 1 Any question about the proportion of observations in a particular interval can be answered by finding the area under the curve. Turn to Table A in the front of your text. Note that table A always gives the area to the left of the z-score. 1 .9066 .0934 Calculator: 2nd VARS (DISTR) 2:normalcdf( ENTER normalcdf(lower limit, upper limit) normalcdf(1.32, 10000) .0934 .8413 .2843 .5570 normalcdf(-.57, 1) .5570 Normal Distribution Calculations We can answer any question about proportions of observations in a Normal distribution by ____________ standardizing and then using the Standard Normal table. 240 170 z 2.33 30 1 .9901 .0099 Calculator: normalcdf(240,10000, , ) normalcdf(240, 10000, 170, 30) .0098 150 170 z .67 30 190 170 z .67 30 .7486 .2514 .4972 Calculator: normalcdf(150,190,170,30) .4950 x 170 .67 30 .67 x 149.9 Calculator: 2nd VARS (DISTR) 3: invNorm( ENTER invNorm(area to left, , ) invNorm(.25, 170, 30) x 149.765 x 170 .84 30 x 195.2 .84 invNorm(.8, 170, 30) x 195.249