正態(tài)分布z值表

1、正態(tài)分布z值表見最下文首先我們得先來了解一下什么是正態(tài)分布：3.8 4.0 4.2 4.4 “ 4.8 5.0 52 5.4 5.6 52 6 紅紗畝故(xlOTL)2252015105g*s1.正態(tài)曲線(normal curve)353025120"|510圖21圖31圖32正態(tài)曲線是簇曲線，呈對(duì)稱鐘形，均數(shù)所在處最高，兩側(cè)逐漸下 降,兩端在無窮處與橫軸無限接近。橫坐標(biāo)常使用觀察值組段，縱坐 標(biāo)常使用頻數(shù)、頻率及概率密度（頻率與組!?巨之比2.正態(tài)分布特征曲線概率密度函數(shù)：_（用_小/（X） =C 2/_ 8 < X V +8c J2ti式中，有4個(gè)常數(shù)，M為總體均數(shù)，o為總

2、體標(biāo)準(zhǔn)差，tt為圓周率，e為自然對(duì)數(shù) 的底數(shù),其中|J、o為不確定的常數(shù)，稱為正態(tài)分布的參數(shù)。M是位置參數(shù)，決定著正態(tài)曲線在X軸上的位置；a是形狀參數(shù)，決定著正態(tài)曲線的分布形狀由此決定的正態(tài)分布記作N（jq2）。僅X為隨機(jī)變量。曲線位置形狀與面積特征：正態(tài)分布曲統(tǒng)(5=1)標(biāo)準(zhǔn)差一樣規(guī)定了曲線的形狀相同，而均數(shù)不同，會(huì)使得曲線在均數(shù)不變，標(biāo)準(zhǔn)差改變，標(biāo)準(zhǔn)差小的曲線變異度小，曲線形狀就 高瘦一點(diǎn);標(biāo)準(zhǔn)差大的變異度大，曲線形狀就矮胖一點(diǎn)。標(biāo)準(zhǔn)正態(tài)分布均數(shù)為0標(biāo)準(zhǔn)差為1的正態(tài)分布被稱為標(biāo)準(zhǔn)正態(tài)分布(standard normal distribution)o對(duì)于任意一個(gè)服從正態(tài)分布N (|j , L

3、)的隨機(jī)變量，可做標(biāo)準(zhǔn)化轉(zhuǎn)換。X JJz =a通過標(biāo)準(zhǔn)化轉(zhuǎn)換后，任意一個(gè)正態(tài)分布曲線下面積求解問題都能 轉(zhuǎn)換成標(biāo)準(zhǔn)正態(tài)分布曲線下面積求解問題。如下所示:2 標(biāo)準(zhǔn)正態(tài)分布的應(yīng)用當(dāng)Z的取值范圍為(Z1,Z2)時(shí)，概率(面積)計(jì)算公式應(yīng)為:P(Z1<Z<Z2) =cp ( Z2 ) - cp ( Z1)因?yàn)榻y(tǒng)計(jì)表中只有Z值的左側(cè)尾部面積，所以根據(jù)上圖所示，當(dāng)Z>0時(shí)應(yīng)有:q)(Z) =l-cp( -Z)所以對(duì)于一個(gè)一般的正態(tài)分布問題，我們可以先通過標(biāo)準(zhǔn)化轉(zhuǎn)換 求得Z值，然后查表找到所對(duì)應(yīng)的值后代入面積公式即可進(jìn)行求解。注意 曲線下面積總和為lo 曲線下的面積是從-8積分到當(dāng)前Z的面

4、積。 曲線下對(duì)稱于0的區(qū)間，面積相等。 當(dāng)和X已知時(shí)，先求Z值，再用Z值查表，得到所求區(qū)間占總面積比例。當(dāng)M/o未知時(shí),要用樣本均數(shù)和樣本標(biāo)準(zhǔn)差S來估計(jì)Z值。 如存在Z值 0 ,應(yīng)該先將其轉(zhuǎn)化為負(fù)值部分再進(jìn)行求解。 如下正態(tài)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