Area under standard normal distribution z 20.00-0.02-0.04-0.06-0.08 3.00.00130.00130.00120.00l10.0010 2.50.00620.00590.00550.00520.0049 -2.00.02280.02170.02070.01970.0188 -1.90.02870.02740.02620.02500.0239 1.60.05480.05260.05050.04850.0465 1.0015870.15390.14920.14460.1401 0.50.30850.30150.29460.28770.2810 00.50000.49200.48400.47610.4681 Z is the standard score, that is the units of standard deviation
16 Area under standard normal distribution (Z) Z 0.00 -0.02 -0.04 -0.06 -0.08 -3.0 0.0013 0.0013 0.0012 0.0011 0.0010 -2.5 0.0062 0.0059 0.0055 0.0052 0.0049 -2.0 0.0228 0.0217 0.0207 0.0197 0.0188 -1.9 0.0287 0.0274 0.0262 0.0250 0.0239 -1.6 0.0548 0.0526 0.0505 0.0485 0.0465 -1.0 0.1587 0.1539 0.1492 0.1446 0.1401 -0.5 0.3085 0.3015 0.2946 0.2877 0.2810 0 0.5000 0.4920 0.4840 0.4761 0.4681 Z 0 Z is the standard score, that is the units of standard deviation
Figure Standard normal curve and some important divisions. 99,74 99,5% P(-1<z<1)=06826 P(-2<z<2)=09545 P(-3<z<3)=0.9974 +2 17
Figure Standard normal curve and some important divisions. 17 •P(-1 < z < 1)=0.6826 •P(-2 < z < 2)=0.9545 •P(-3 < z < 3)=0.9974
Find probability in EXcel a Using an electronic table, find the area under the standard normal density to the left of 2. 824 a We use the exce 2007 function normsdist evaluated at 2.824 [NORMSDIST(2. 824)with the result as follows c 开始插入 公式数据审阅 Pr(1.0≤z≤1.58)=Pr(0≤z≤1.58)-Pr(0≤z≤1.0 f∑自 0.4429-0.3413 插入函数自动求和最近使用财务逻文本日期和查找与 的函数 时间·引用 0.1016 B2 S=NORMSDIST(A2) B C D E 22.824D0998 18
Find probability in Excel Using an electronic table, find the area under the standard normal density to the left of 2.824. We use the excel2007 function NORMSDIST evaluated at 2.824 [NORMSDIST(2.824)]with the result as follows: 18
EXAMPLE a What is the probability of obtaining a z value between 1.0 and 1.582 a We have 19
EXAMPLE What is the probability of obtaining a z value between 1.0 and 1.58? We have 19
CUMULATIVE PROBABILITY FOR X-N(,o2) 日Z(X-1)oX=叶+Zo 吃可平“0 30120101+0+20+3x
CUMULATIVE PROBABILITY FOR X~N(μ,σ 2 ) Z=(X-μ)/σ X= μ+Zσ 20 -3 -2 - + +2 +3 x