正态分布z值表

1、正态分布z值表见最下文首先我们得先来了解一下什么是正态分布：3.8 4.0 4.2 4.4 “ 4.8 5.0 52 5.4 5.6 52 6 红紗畝故(xlOTL)2252015105g*s1.正态曲线(normal curve)353025120"|510图21图31图32正态曲线是簇曲线，呈对称钟形，均数所在处最高，两侧逐渐下 降,两端在无穷处与横轴无限接近。横坐标常使用观察值组段，纵坐 标常使用频数、频率及概率密度（频率与组!?巨之比2.正态分布特征曲线概率密度函数：_（用_小/（X） =C 2/_ 8 < X V +8c J2ti式中，有4个常数，M为总体均数，o为总

2、体标准差，tt为圆周率，e为自然对数 的底数,其中|J、o为不确定的常数，称为正态分布的参数。M是位置参数，决定着正态曲线在X轴上的位置；a是形状参数，决定着正态曲线的分布形状由此决定的正态分布记作N（jq2）。仅X为随机变量。曲线位置形状与面积特征：正态分布曲统(5=1)标准差一样规定了曲线的形状相同，而均数不同，会使得曲线在均数不变，标准差改变，标准差小的曲线变异度小，曲线形状就 高瘦一点;标准差大的变异度大，曲线形状就矮胖一点。标准正态分布均数为0标准差为1的正态分布被称为标准正态分布(standard normal distribution)o对于任意一个服从正态分布N (|j , L

3、)的随机变量，可做标准化转换。X JJz =a通过标准化转换后，任意一个正态分布曲线下面积求解问题都能 转换成标准正态分布曲线下面积求解问题。如下所示:2 标准正态分布的应用当Z的取值范围为(Z1,Z2)时，概率(面积)计算公式应为:P(Z1<Z<Z2) =cp ( Z2 ) - cp ( Z1)因为统计表中只有Z值的左侧尾部面积，所以根据上图所示，当Z>0时应有:q)(Z) =l-cp( -Z)所以对于一个一般的正态分布问题，我们可以先通过标准化转换 求得Z值，然后查表找到所对应的值后代入面积公式即可进行求解。注意 曲线下面积总和为lo 曲线下的面积是从-8积分到当前Z的面

4、积。 曲线下对称于0的区间，面积相等。 当和X已知时，先求Z值，再用Z值查表，得到所求区间占总面积比例。当M/o未知时,要用样本均数和样本标准差S来估计Z值。 如存在Z值 0 ,应该先将其转化为负值部分再进行求解。 如下正态分布z值表0.000.010.020.030.040.050.060.070.080.090.00.50000.50400.50800.51200.51600.51990.52390.52790.53190.53590.10.5398(L54380.5478().55170.55570.55960.56360.56750.57140.57530.20.57930.58320

5、.58710.59100.59480.59870.6026O.6C640.61030.61410.30.61790.62170.62550.62930.63310.63680.64060.64430.64800.65170.40.65540.65910.G6280.GG640.67030.67360.67720.68080.68440.68790.50.69150.69500.G9850.70190.70540.70880.71230.71570.71900.72240.60.72570.72910.73240.73570.73890.74220.74540.74860.75170.75490

6、.70.75800.76110.76420.76730.77040.77340.77640.77940.78230.78520.80.78810.79100.79390.79670.79950.80230.80510.80780.81060.81330.90.81590.81860.82120.R23R0.82640.82890.83150.83400.83650.83891.00.84130.84380.8461084850.85080.85310.85540.85770.85990.86211.10.86430.86650.86860.87080.87290.87490.87700.879

7、00.88100.88301.20.88490.88G90.88880.89070.89250.89440.89G20.89800.89970.90151.30.90320.90490.906G0.90820.90990.91150.91310.91470.91620.91771.40.91920.92070.92220.92360.92510.92650.92790.92920.93060.93191.50.93320.93450.93570.93700.93820.93940.94060.94180.94290.94411.60.94520.94630.94740.94840.94950.

8、95050.95150.95250.95350.95451.70.95540.95640.95730.95820.95910.95990.96080.96160.96250.96331.80.96410.96490.96560.96640.96710.96780.96S60.96930.96990.97061.90.97130.97190.97260.97320.97380.97440.97500.97560.97610.97672.00.97720.97780.97830.97880.97930.97980.98030.98080.98120.98172.10.98210.982G0.983

9、00.98340.98380.98420.98460.98500.98540.98572.20.98G10.98640.98680.98710.98750.98780.98810.98840.98870.98902.30.98930.98960.98980.99010.99040.99060.99090.99110.99130.9916240.99180.99200.99220.99250.99270.99290.99310.99320.99340.99362.50.99380.99400.99410.9130.99450.99460.99480.99490.99510.99522.60.99530.99550.99560.99570.99590.99600.99610.99620.99630.99642.70.99650.99660.99670.99680.99690.99700.99710.99720.99730.99742.80.99740.99750.99760.99770.99770.9978