概率论与数理统计浙大高教社电子教案第七章7

1、第五节 正态总体均值与方差的区间估计一、单个总体的情况二、两个总体的情况三、小结一、单个总体 的情况由上节例2可知:1. 包糖机某日开工包了12包糖,称得质量(单位:克)分别为506,500,495,488,504,486,505,513,521,520,512,485. 假设重量服从正态分布,解附表2-1例1附表2-2查表得推导过程如下:解 有一大批糖果,现从中随机地取16袋, 称得重量(克)如下: 设袋装糖果的重量服从正态分布, 试求总体均值附表3-1例2就是说估计袋装糖果重量的均值在500.4克与507.1克之间, 这个估计的可信程度为95%.这个误差的可信度为95%.解附表3-2例3(

2、续例1)如果只假设糖包的重量服从正态分布解例4推导过程如下:根据第六章第二节定理二知2.进一步可得:注意: 在密度函数不对称时, 习惯上仍取对称的分位点来确定置信区间(如图). (续例2) 求例2中总体标准差 的置信度为0.95的置信区间.解代入公式得标准差的置信区间附表4-1附表4-2例5解例6 (续例1)二、两个总体 的情况讨论两个整体总体均值差和方差比的估计问题.推导过程如下:1.例7为比较, 两种型号步枪子弹的枪口速度,随机地取型子弹10发, 得到枪口速度的平均值为随机地取型子弹20发, 得枪口速度平均值为假设两总体都可认为近似地服从正态分布,且由生产过程可认为它们的方差相等, 求两总

3、体均值差信区间.解由题意, 两总体样本独立且方差相等(但未知),解由题意, 两总体样本独立且方差相等(但未知),例8为提高某一化学生产过程的得率, 试图采用一种新的催化剂, 为慎重起见, 在试验工厂先进行体都可认为近似地服从正态分布, 且方差相等, 求两总体均值差试验. 设采用原来的催化剂进行了次试验,得到得率的平均值又采用新的催化剂进行了次试验,得到得率的平均值假设两总推导过程如下:2.根据F分布的定义, 知解例9研究由机器 A 和机器 B 生产的钢管内径, 随机抽取机器 A 生产的管子 18 只, 测得样本方差为均未知, 求方差比区间.设两样本相互独抽取机器B生产的管子 13 只, 测得样

4、本方差为立,且设由机器 A 和机器 B 生产的钢管内径分别服从正态分布信解例10甲、乙两台机床加工同一种零件, 在机床甲加工的零件中抽取9个样品, 在机床乙加工的零件信区间. 假定测量值都服从正态分布, 方差分别为的置在置信度由所给数据算得0.98下, 试求这两台机床加工精度之比中抽取6个样品,并分别测得它们的长度(单位:mm),三、小结附表2-1标准正态分布表z01234567890.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.60.50000.53980.57930.61790.65540.69150.72570.75800.78810.

5、81590.84130.86430.88490.90320.91920.93320.94520.50400.54380.58320.62170.65910.69500.72910.76110.79100.81860.84380.86650.88690.90490.92070.93450.94630.50800.54780.58710.62550.66280.69850.73240.76420.79390.82120.84610.86860.88880.90660.92220.93570.94740.51200.55170.59100.62930.66640.70190.73570.76730.

6、79670.82380.84850.87080.89070.90820.92360.93700.94840.51600.55570.59480.63310.67000.70540.73890.77030.79950.82640.85080.87290.89250.90990.92510.93820.94950.51990.55960.59870.63680.67360.70880.74220.77340.80230.82890.85310.87490.89440.91150.92650.93940.95050.52390.56360.60260.64060.67720.71230.74540.

7、77640.80510.83150.85540.87700.89620.91310.92780.94060.95150.52790.56750.60640.64430.68080.71570.74860.77940.80780.83400.85770.87900.89800.91470.92920.94180.95250.53190.57140.61030.64800.68440.71900.75170.78230.81060.83650.85990.88100.89970.91620.93060.94300.95350.53590.57530.61410.65170.68790.72240.

8、75490.78520.81330.83890.86210.88300.90150.91770.93190.94410.95451.645z01234567891.61.71.81.92.02.12.22.32.42.52.62.72.82.93.00.94520.95540.96410.97130.97720.98210.98610.98930.99180.99380.99530.99650.99740.99810.99870.94630.95640.96480.97190.97780.98260.98640.98960.99200.99400.99550.99660.99750.99820

9、.99900.94740.95730.96560.97260.97830.98300.98680.98980.99220.99410.99560.99670.99760.99820.99930.94840.95820.96640.97320.97880.98340.98710.99010.99250.99430.99570.99680.99770.99830.99950.94950.95910.96710.97380.97930.98380.98710.99040.99270.99450.99590.99690.99770.99840.99970.95050.95990.96780.97440

10、.97980.98420.98780.99060.99290.99460.99600.99700.99780.99840.99980.95150.96080.96860.97500.98030.98460.98810.99090.99310.99480.99610.99710.99790.99850.99980.95250.96160.96930.97560.98080.98500.98840.99110.99320.99490.99620.99720.99790.99850.99990.95350.96250.97000.97620.98120.98540.98870.99130.99340

11、.99510.99630.99730.99800.99860.99990.95450.96330.97060.97670.98170.98580.98900.99160.99360.99520.99640.99740.99810.99861.00001.96附表2-2标准正态分布表附表3-1 =0.250.100.050.0250.010.005123456789101112131415161.00000.81650.76490.74070.72670.71760.71110.70640.70270.69980.69740.69550.69380.69240.69120.69013.07771

12、.88561.63771.53321.47591.43981.41491.39681.38301.37221.36341.35621.35021.34501.34061.33686.31382.92002.35342.13182.01501.94321.89461.85951.83311.81251.79591.78231.77091.76131.75311.745912.7062 4.3027 3.1824 2.7764 2.5706 2.4469 2.3646 2.3060 2.2622 2.2281 2.2010 2.1788 2.1604 2.1448 2.1315 2.119931.

13、8207 6.9646 4.5407 3.7469 3.3649 3.1427 2.9980 2.8965 2.8214 2.7638 2.7181 2.6810 2.6503 2.6245 2.6025 2.583563.6574 9.9248 5.8409 4.6041 4.0322 3.7074 3.4995 3.3554 3.2498 3.1693 3.1058 3.0545 3.0123 2.9768 2.9467 2.9208分布表2.1315 =0.250.100.050.0250.010.005123456789101112131415161.00000.81650.76490

14、.74070.72670.71760.71110.70640.70270.69980.69740.69550.69380.69240.69120.69013.07771.88561.63771.53321.47591.43981.41491.39681.38301.37221.36341.35621.35021.34501.34061.33686.31382.92002.35342.13182.01501.94321.89461.85951.83311.81251.79591.78231.77091.76131.75311.745912.7062 4.3027 3.1824 2.7764 2.

15、5706 2.4469 2.3646 2.3060 2.2622 2.2281 2.2010 2.1788 2.1604 2.1448 2.1315 2.119931.8207 6.9646 4.5407 3.7469 3.3649 3.1427 2.9980 2.8965 2.8214 2.7638 2.7181 2.6810 2.6503 2.6245 2.6025 2.583563.6574 9.9248 5.8409 4.6041 4.0322 3.7074 3.4995 3.3554 3.2498 3.1693 3.1058 3.0545 3.0123 2.9768 2.9467 2

16、.92082.2010附表3-2分布表附表4-2=0.9950.990.9750.950.900.75123456789101112131415160.0100.0720.2070.4120.6760.9891.3441.7352.1562.6033.0743.5654.0754.6015.1420.0200.1150.2970.5540.8721.2391.6462.0882.5583.0533.5714.1074.6605.2295.8120.0010.0510.2160.4840.8311.2371.6902.1802.7003.2473.8164.4045.0095.6296.2626

17、.9080.0040.1030.3520.7111.1451.6352.1672.7333.3253.9404.5755.2265.8926.5717.2617.9620.0160.2110.5841.0641.6102.2042.8333.4904.1684.8655.5786.3047.0427.7908.5479.3120.1020.5751.2131.9232.6753.4554.2555.0715.8996.7377.5848.4389.29910.16511.03711.912分布表6.262附表4-1=0.250.100.050.0250.010.005123456789101112131415161.3232.7734.1085.3856.6267.8419.03710.21911.38912.54913.70114.84515.98417.11718.24519.3692.7064.6056.2517.7799.23610.64512.01713.36214.68415.98717.27518.54919.81220.06422.30723.5423.8415.9917.8159.48811.07112.59214.06715.50716.91918.30719.67521.02622.36223.68524.99626.2965.0247.3