{"id":223,"date":"2023-08-04T00:20:17","date_gmt":"2023-08-04T00:20:17","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e6%ad%a3%e6%80%81%e5%88%86%e5%b8%83%e8%a1%a8\/"},"modified":"2023-08-04T00:20:17","modified_gmt":"2023-08-04T00:20:17","slug":"%e6%ad%a3%e6%80%81%e5%88%86%e5%b8%83%e8%a1%a8","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e6%ad%a3%e6%80%81%e5%88%86%e5%b8%83%e8%a1%a8\/","title":{"rendered":"\u6b63\u6001\u5206\u5e03\u8868"},"content":{"rendered":"

\u5728\u672c\u6587\u4e2d\uff0c\u60a8\u5c06\u627e\u5230\u6b63\u6001\u5206\u5e03\u8868\uff0c\u6b64\u5916\u8fd8\u6709\u4e00\u4e9b\u6709\u5173\u5982\u4f55\u4f7f\u7528\u6b63\u6001\u5206\u5e03\u8868\u7684\u8bf4\u660e\u3002 <\/p>\n

<\/span>\u6b63\u6001\u5206\u5e03\u8868\u503c<\/span><\/h2>\n

\u4e0b\u8868\u663e\u793a\u4e86\u6b63\u6001\u5206\u5e03\uff08\u5de6\u5c3e\uff09\u7684\u7d2f\u79ef\u6982\u7387\u503c\u3002\u8bf7\u6ce8\u610f\uff0c\u6b64\u8868\u4e2d\u7684\u503c\u5bf9\u5e94\u4e8e\u6807\u51c6\u6b63\u6001\u5206\u5e03\uff0c\u56e0\u6b64\u8981\u4f7f\u7528\u8be5\u8868\uff0c\u5fc5\u987b\u9996\u5148\u8f93\u5165\u53d8\u91cf<\/a>\u3002 <\/p>\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
z<\/th>\n 0.00<\/th>\n 0.01<\/th>\n 0.02<\/th>\n 0.03<\/th>\n 0.04<\/th>\n 0.05<\/th>\n 0.06<\/th>\n 0.07<\/th>\n 0.08<\/th>\n 0.09<\/th>\n<\/tr>\n
0.0<\/th>\n 0.5000<\/td>\n 0.5040<\/td>\n 0.5080<\/td>\n 0.5120<\/td>\n 0.5160<\/td>\n 0.5199<\/td>\n 0.5239<\/td>\n 0.5279<\/td>\n 0.5319<\/td>\n 0.5359<\/td>\n<\/tr>\n
0.1<\/th>\n 0.5398<\/td>\n 0.5438<\/td>\n 0.5478<\/td>\n 0.5517<\/td>\n 0.5557<\/td>\n 0.5596<\/td>\n 0.5636<\/td>\n 0.5675<\/td>\n 0.5714<\/td>\n 0.5753<\/td>\n<\/tr>\n
0.2<\/th>\n 0.5793<\/td>\n 0.5832<\/td>\n 0.5871<\/td>\n 0.5910<\/td>\n 0.5948<\/td>\n 0.5987<\/td>\n 0.6026<\/td>\n 0.6064<\/td>\n 0.6103<\/td>\n 0.6141<\/td>\n<\/tr>\n
0.3<\/th>\n 0.6179<\/td>\n 0.6217<\/td>\n 0.6255<\/td>\n 0.6293<\/td>\n 0.6331<\/td>\n 0.6368<\/td>\n 0.6406<\/td>\n 0.6443<\/td>\n 0.6480<\/td>\n 0.6517<\/td>\n<\/tr>\n
0.4<\/th>\n 0.6554<\/td>\n 0.6591<\/td>\n 0.6628<\/td>\n 0.6664<\/td>\n 0.6700<\/td>\n 0.6736<\/td>\n 0.6772<\/td>\n 0.6808<\/td>\n 0.6844<\/td>\n 0.6879<\/td>\n<\/tr>\n
0.5<\/th>\n 0.6915<\/td>\n 0.6950<\/td>\n 0.6985<\/td>\n 0.7019<\/td>\n 0.7054<\/td>\n 0.7088<\/td>\n 0.7123<\/td>\n 0.7157<\/td>\n 0.7190<\/td>\n 0.7224<\/td>\n<\/tr>\n
0.6<\/th>\n 0.7257<\/td>\n 0.7291<\/td>\n 0.7324<\/td>\n 0.7357<\/td>\n 0.7389<\/td>\n 0.7422<\/td>\n 0.7454<\/td>\n 0.7486<\/td>\n 0.7517<\/td>\n 0.7549<\/td>\n<\/tr>\n
0.7<\/th>\n 0.7580<\/td>\n 0.7611<\/td>\n 0.7642<\/td>\n 0.7673<\/td>\n 0.7704<\/td>\n 0.7734<\/td>\n 0.7764<\/td>\n 0.7794<\/td>\n 0.7823<\/td>\n 0.7852<\/td>\n<\/tr>\n
0.8<\/th>\n 0.7881<\/td>\n 0.7910<\/td>\n 0.7939<\/td>\n 0.7967<\/td>\n 0.7995<\/td>\n 0.8023<\/td>\n 0.8051<\/td>\n 0.8078<\/td>\n 0.8106<\/td>\n 0.8133<\/td>\n<\/tr>\n
0.9<\/th>\n 0.8159<\/td>\n 0.8186<\/td>\n 0.8212<\/td>\n 0.8238<\/td>\n 0.8264<\/td>\n 0.8289<\/td>\n 0.8315<\/td>\n 0.8340<\/td>\n 0.8365<\/td>\n 0.8389 <\/td>\n<\/tr>\n
<\/th>\n 0.00<\/th>\n 0.01<\/th>\n 0.02<\/th>\n 0.03<\/th>\n 0.04<\/th>\n 0.05<\/th>\n 0.06<\/th>\n 0.07<\/th>\n 0.08<\/th>\n 0.09<\/th>\n<\/tr>\n
1.0<\/th>\n 0.8413<\/td>\n 0.8438<\/td>\n 0.8461<\/td>\n 0.8485<\/td>\n 0.8508<\/td>\n 0.8531<\/td>\n 0.8554<\/td>\n 0.8577<\/td>\n 0.8599<\/td>\n 0.8621<\/td>\n<\/tr>\n
1.1<\/th>\n 0.8643<\/td>\n 0.8665<\/td>\n 0.8686<\/td>\n 0.8708<\/td>\n 0.8729<\/td>\n 0.8749<\/td>\n 0.8770<\/td>\n 0.8790<\/td>\n 0.8810<\/td>\n 0.8830<\/td>\n<\/tr>\n
1.2<\/th>\n 0.8849<\/td>\n 0.8869<\/td>\n 0.8888<\/td>\n 0.8907<\/td>\n 0.8925<\/td>\n 0.8944<\/td>\n 0.8962<\/td>\n 0.8980<\/td>\n 0.8997<\/td>\n 0.9015<\/td>\n<\/tr>\n
1.3<\/th>\n 0.9032<\/td>\n 0.9049<\/td>\n 0.9066<\/td>\n 0.9082<\/td>\n 0.9099<\/td>\n 0.9115<\/td>\n 0.9131<\/td>\n 0.9147<\/td>\n 0.9162<\/td>\n 0.9177<\/td>\n<\/tr>\n
1.4<\/th>\n 0.9192<\/td>\n 0.9207<\/td>\n 0.9222<\/td>\n 0.9236<\/td>\n 0.9251<\/td>\n 0.9265<\/td>\n 0.9279<\/td>\n 0.9292<\/td>\n 0.9306<\/td>\n 0.9319<\/td>\n<\/tr>\n
1.5<\/th>\n 0.9332<\/td>\n 0.9345<\/td>\n 0.9357<\/td>\n 0.9370<\/td>\n 0.9382<\/td>\n 0.9394<\/td>\n 0.9406<\/td>\n 0.9418<\/td>\n 0.9429<\/td>\n 0.9441<\/td>\n<\/tr>\n
1.6<\/th>\n 0.9452<\/td>\n 0.9463<\/td>\n 0.9474<\/td>\n 0.9484<\/td>\n 0.9495<\/td>\n 0.9505<\/td>\n 0.9515<\/td>\n 0.9525<\/td>\n 0.9535<\/td>\n 0.9545<\/td>\n<\/tr>\n
1.7<\/th>\n 0.9554<\/td>\n 0.9564<\/td>\n 0.9573<\/td>\n 0.9582<\/td>\n 0.9591<\/td>\n 0.9599<\/td>\n 0.9608<\/td>\n 0.9616<\/td>\n 0.9625<\/td>\n 0.9633<\/td>\n<\/tr>\n
1.8<\/th>\n 0.9641<\/td>\n 0.9649<\/td>\n 0.9656<\/td>\n 0.9664<\/td>\n 0.9671<\/td>\n 0.9678<\/td>\n 0.9686<\/td>\n 0.9693<\/td>\n 0.9699<\/td>\n 0.9706<\/td>\n<\/tr>\n
1.9<\/th>\n 0.9713<\/td>\n 0.9719<\/td>\n 0.9726<\/td>\n 0.9732<\/td>\n 0.9738<\/td>\n 0.9744<\/td>\n 0.9750<\/td>\n 0.9756<\/td>\n 0.9761<\/td>\n 0.9767 <\/td>\n<\/tr>\n
<\/th>\n 0.00<\/th>\n 0.01<\/th>\n 0.02<\/th>\n 0.03<\/th>\n 0.04<\/th>\n 0.05<\/th>\n 0.06<\/th>\n 0.07<\/th>\n 0.08<\/th>\n 0.09<\/th>\n<\/tr>\n
2.0<\/th>\n 0.9772<\/td>\n 0.9778<\/td>\n 0.9783<\/td>\n 0.9788<\/td>\n 0.9793<\/td>\n 0.9798<\/td>\n 0.9803<\/td>\n 0.9808<\/td>\n 0.9812<\/td>\n 0.9817<\/td>\n<\/tr>\n
2.1<\/th>\n 0.9821<\/td>\n 0.9826<\/td>\n 0.9830<\/td>\n 0.9834<\/td>\n 0.9838<\/td>\n 0.9842<\/td>\n 0.9846<\/td>\n 0.9850<\/td>\n 0.9854<\/td>\n 0.9857<\/td>\n<\/tr>\n
2.2<\/th>\n 0.9861<\/td>\n 0.9864<\/td>\n 0.9868<\/td>\n 0.9871<\/td>\n 0.9875<\/td>\n 0.9878<\/td>\n 0.9881<\/td>\n 0.9884<\/td>\n 0.9887<\/td>\n 0.9890<\/td>\n<\/tr>\n
23<\/th>\n 0.9893<\/td>\n 0.9896<\/td>\n 0.9898<\/td>\n 0.9901<\/td>\n 0.9904<\/td>\n 0.9906<\/td>\n 0.9909<\/td>\n 0.9911<\/td>\n 0.9913<\/td>\n 0.9916<\/td>\n<\/tr>\n
2.4<\/th>\n 0.9918<\/td>\n 0.9920<\/td>\n 0.9922<\/td>\n 0.9925<\/td>\n 0.9927<\/td>\n 0.9929<\/td>\n 0.9931<\/td>\n 0.9932<\/td>\n 0.9934<\/td>\n 0.9936<\/td>\n<\/tr>\n
2.5<\/th>\n 0.9938<\/td>\n 0.9940<\/td>\n 0.9941<\/td>\n 0.9943<\/td>\n 0.9945<\/td>\n 0.9946<\/td>\n 0.9948<\/td>\n 0.9949<\/td>\n 0.9951<\/td>\n 0.9952<\/td>\n<\/tr>\n
2.6<\/th>\n 0.9953<\/td>\n 0.9955<\/td>\n 0.9956<\/td>\n 0.9957<\/td>\n 0.9959<\/td>\n 0.9960<\/td>\n 0.9961<\/td>\n 0.9962<\/td>\n 0.9963<\/td>\n 0.9964<\/td>\n<\/tr>\n
2.7<\/th>\n 0.9965<\/td>\n 0.9966<\/td>\n 0.9967<\/td>\n 0.9968<\/td>\n 0.9969<\/td>\n 0.9970<\/td>\n 0.9971<\/td>\n 0.9972<\/td>\n 0.9973<\/td>\n 0.9974<\/td>\n<\/tr>\n
2.8<\/th>\n 0.9974<\/td>\n 0.9975<\/td>\n 0.9976<\/td>\n 0.9977<\/td>\n 0.9977<\/td>\n 0.9978<\/td>\n 0.9979<\/td>\n 0.9979<\/td>\n 0.9980<\/td>\n 0.9981<\/td>\n<\/tr>\n
2.9<\/th>\n 0.9981<\/td>\n 0.9982<\/td>\n 0.9982<\/td>\n 0.9983<\/td>\n 0.9984<\/td>\n 0.9984<\/td>\n 0.9985<\/td>\n 0.9985<\/td>\n 0.9986<\/td>\n 0.9986 <\/td>\n<\/tr>\n
<\/th>\n 0.00<\/th>\n 0.01<\/th>\n 0.02<\/th>\n 0.03<\/th>\n 0.04<\/th>\n 0.05<\/th>\n 0.06<\/th>\n 0.07<\/th>\n 0.08<\/th>\n 0.09<\/th>\n<\/tr>\n
3<\/th>\n 0.9987<\/td>\n 0.9987<\/td>\n 0.9987<\/td>\n 0.9988<\/td>\n 0.9988<\/td>\n 0.9989<\/td>\n 0.9989<\/td>\n 0.9989<\/td>\n 0.9990<\/td>\n 0.9990<\/td>\n<\/tr>\n
3.1<\/th>\n 0.9990<\/td>\n 0.9991<\/td>\n 0.9991<\/td>\n 0.9991<\/td>\n 0.9992<\/td>\n 0.9992<\/td>\n 0.9992<\/td>\n 0.9992<\/td>\n 0.9993<\/td>\n 0.9993<\/td>\n<\/tr>\n
3.2<\/th>\n 0.9993<\/td>\n 0.9993<\/td>\n 0.9994<\/td>\n 0.9994<\/td>\n 0.9994<\/td>\n 0.9994<\/td>\n 0.9994<\/td>\n 0.9995<\/td>\n 0.9995<\/td>\n 0.9995<\/td>\n<\/tr>\n
3.3<\/th>\n 0.9995<\/td>\n 0.9995<\/td>\n 0.9995<\/td>\n 0.9996<\/td>\n 0.9996<\/td>\n 0.9996<\/td>\n 0.9996<\/td>\n 0.9996<\/td>\n 0.9996<\/td>\n 0.9997<\/td>\n<\/tr>\n
3.4<\/th>\n 0.9997<\/td>\n 0.9997<\/td>\n 0.9997<\/td>\n 0.9997<\/td>\n 0.9997<\/td>\n 0.9997<\/td>\n 0.9997<\/td>\n 0.9997<\/td>\n 0.9997<\/td>\n 0.9998<\/td>\n<\/tr>\n
3.5<\/th>\n 0.9998<\/td>\n 0.9998<\/td>\n 0.9998<\/td>\n 0.9998<\/td>\n 0.9998<\/td>\n 0.9998<\/td>\n 0.9998<\/td>\n 0.9998<\/td>\n 0.9998<\/td>\n 0.9998<\/td>\n<\/tr>\n
3.6<\/th>\n 0.9998<\/td>\n 0.9998<\/td>\n 0.9999<\/td>\n 0.9999<\/td>\n 0.9999<\/td>\n 0.9999<\/td>\n 0.9999<\/td>\n 0.9999<\/td>\n 0.9999<\/td>\n 0.9999<\/td>\n<\/tr>\n
3.7<\/th>\n 0.9999<\/td>\n 0.9999<\/td>\n 0.9999<\/td>\n 0.9999<\/td>\n 0.9999<\/td>\n 0.9999<\/td>\n 0.9999<\/td>\n 0.9999<\/td>\n 0.9999<\/td>\n 0.9999<\/td>\n<\/tr>\n
3.8<\/th>\n 0.9999<\/td>\n 0.9999<\/td>\n 0.9999<\/td>\n 0.9999<\/td>\n 0.9999<\/td>\n 0.9999<\/td>\n 0.9999<\/td>\n 0.9999<\/td>\n 0.9999<\/td>\n 0.9999<\/td>\n<\/tr>\n
3.9<\/th>\n 1.0000<\/td>\n 1.0000<\/td>\n 1.0000<\/td>\n 1.0000<\/td>\n 1.0000<\/td>\n 1.0000<\/td>\n 1.0000<\/td>\n 1.0000<\/td>\n 1.0000<\/td>\n 1.0000 <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n

<\/span>\u5982\u4f55\u4f7f\u7528\u6b63\u6001\u5206\u5e03\u8868<\/span><\/h2>\n

\u8981\u4f7f\u7528\u6b63\u6001\u5206\u5e03\u8868\uff0c\u5fc5\u987b\u6267\u884c\u4ee5\u4e0b\u6b65\u9aa4\uff1a<\/p>\n

    \n
  1. \u6807\u51c6\u5316\uff08\u6216\u5178\u578b\u5316\uff09\u6b63\u6001\u5206\u5e03\u7684\u503c\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u9700\u8981\u51cf\u53bb\u8be5\u503c\u51cf\u53bb\u6b63\u6001\u5206\u5e03\u7684\u5747\u503c\uff0c\u7136\u540e\u9664\u4ee5\u6b63\u6001\u5206\u5e03\u7684\u6807\u51c6\u5dee\u3002<\/span><\/li>\n
  2. \u5c06\u4e0a\u4e00\u6b65\u5f97\u5230\u7684\u503c\u7684\u6574\u6570\u90e8\u5206\u548c\u5c0f\u6570\u70b9\u540e\u4e00\u4f4d\u5bf9\u5e94\u7684\u884c\u586b\u5165\u8868\u683c\u3002<\/span><\/li>\n
  3. \u6309\u6240\u5f97\u503c\u7684\u5c0f\u6570\u70b9\u540e\u7b2c\u4e8c\u4f4d\u7684\u5217\u8f93\u5165\u8868\u683c\u3002<\/span><\/li>\n
  4. \u7d2f\u79ef\u6982\u7387\u503c\u662f\u5728\u5148\u524d\u6b65\u9aa4\u4e2d\u7684\u884c\u548c\u5217\u76f8\u4ea4\u5904\u627e\u5230\u7684\u503c\u3002<\/span><\/li>\n<\/ol>\n

    \u8fd9\u6837\u60a8\u5c31\u53ef\u4ee5\u770b\u5230\u4f7f\u7528\u6b63\u6001\u5206\u5e03\u8868\u7684\u793a\u4f8b\uff0c\u4e0b\u9762\u6211\u4eec\u5c06\u5728\u5e73\u5747\u503c\u4e3a 28\u3001\u6807\u51c6\u5dee\u4e3a 7 \u7684\u6b63\u6001\u5206\u5e03\u4e2d\u627e\u5230\u5c0f\u4e8e 33 \u7684\u503c\u7684\u7d2f\u79ef\u6982\u7387\u3002<\/p>\n<\/p>\n

    \"N(28,7)\\<\/p>\n<\/p>\n

    \u4e3a\u4e86\u4f7f\u7528\u6b63\u6001\u5206\u5e03\u8868\uff0c\u6211\u4eec\u5fc5\u987b\u9996\u5148\u6267\u884c\u6253\u5b57\u8fc7\u7a0b\u4ee5\u83b7\u5f97\u6807\u51c6\u6b63\u6001\u5206\u5e03\u3002\u4e3a\u6b64\uff0c\u60a8\u5fc5\u987b\u4ece\u76f8\u5173\u503c\u4e2d\u51cf\u53bb\u5e73\u5747\u503c\uff0c\u7136\u540e\u9664\u4ee5\u5206\u5e03\u7684\u6807\u51c6\u5dee\uff1a<\/p>\n<\/p>\n

    \"Z=\\cfrac{X-\\mu}{\\sigma}\"<\/p>\n<\/p>\n

    \u56e0\u6b64\uff0c\u6211\u4eec\u51cf\u53bb\u5e73\u5747\u503c\u5e76\u5c06\u6982\u7387\u503c\u9664\u4ee5\u6807\u51c6\u5dee\uff1a<\/p>\n<\/p>\n

    \"\\displaystyle<\/p>\n<\/p>\n

    \u4e00\u65e6\u6211\u4eec\u5bf9\u53d8\u91cf\u8fdb\u884c\u4e86\u6807\u51c6\u5316\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u8f6c\u5230\u6807\u51c6\u6b63\u6001\u5206\u5e03\u6982\u7387\u8868\uff08\u89c1\u4e0a\u6587\uff09\u6765\u67e5\u770b 0.71 \u7684\u503c\u5bf9\u5e94\u7684\u6982\u7387\u662f\u591a\u5c11\uff1a<\/p>\n<\/p>\n

    \"\\displaystyle<\/p>\n<\/p>\n

    \u56e0\u6b64\uff0c\u83b7\u5f97\u7b49\u4e8e\u6216\u5c0f\u4e8e 0.71 \u7684\u503c\u7684\u6982\u7387\u4e3a 76.11%\u3002<\/p>\n

    \u8bf7\u8bb0\u4f4f\uff0c\u5982\u679c\u5728\u6b64\u8fc7\u7a0b\u4e2d\u83b7\u5f97\u7684 Z \u503c\u4e3a\u8d1f\u6570\uff0c\u4e3a\u4e86\u8ba1\u7b97\u5176\u6982\u7387\uff0c\u6211\u4eec\u5fc5\u987b\u4ece\u6982\u7387\u4e2d\u51cf\u53bb Z \u7684\u6b63\u503c\u3002\u770b\u4e0b\u9762\u7684\u4f8b\u5b50\uff1a<\/p>\n<\/p>\n

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