{"id":77800,"date":"2026-02-25T14:49:51","date_gmt":"2026-02-25T06:49:51","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/77800.html"},"modified":"2026-02-25T14:49:51","modified_gmt":"2026-02-25T06:49:51","slug":"6-%e5%9f%ba%e4%ba%8e%e6%a6%82%e7%8e%87%e5%88%86%e5%b8%83%e5%87%bd%e6%95%b0%e7%9a%84%e7%bd%ae%e4%bf%a1%e5%8c%ba%e9%97%b4%e5%88%86%e6%9e%90%e4%b8%8e%e6%ad%a3%e6%80%81%e5%88%86%e5%b8%83%e5%8c%ba","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/77800.html","title":{"rendered":"6. \u57fa\u4e8e\u6982\u7387\u5206\u5e03\u51fd\u6570\u7684\u7f6e\u4fe1\u533a\u95f4\u5206\u6790\u4e0e\u6b63\u6001\u5206\u5e03\u533a\u95f4\u6982\u7387\u8ba1\u7b97"},"content":{"rendered":"

\u57fa\u4e8e\u6982\u7387\u5206\u5e03\u51fd\u6570\u7684\u7f6e\u4fe1\u533a\u95f4\u5206\u6790\u4e0e\u6b63\u6001\u5206\u5e03\u533a\u95f4\u6982\u7387\u8ba1\u7b97<\/h2>\n

\u7f6e\u4fe1\u533a\u95f4\u662f\u5236\u9020\u8fc7\u7a0b\u968f\u673a\u5efa\u6a21\u4e0e\u7edf\u8ba1\u8fc7\u7a0b\u63a7\u5236\u4e2d\u7684\u6838\u5fc3\u5e94\u7528\u5de5\u5177\uff0c\u5176\u4ee5\u6982\u7387\u5206\u5e03\u51fd\u6570\uff08 P D F PDF <\/span><\/span>P<\/span>D<\/span>F<\/span><\/span><\/span><\/span><\/span>\uff09\u4e3a\u57fa\u7840\uff0c\u901a\u8fc7\u91cf\u5316\u8fc7\u7a0b\u8f93\u51fa\u5728\u6307\u5b9a\u533a\u95f4\u5185\u7684\u53d6\u503c\u6982\u7387\uff0c\u5b9e\u73b0\u5bf9\u968f\u673a\u8fc7\u7a0b\u8f93\u51fa\u7684\u6982\u7387\u5316\u9884\u6d4b\u4e0e\u7f6e\u4fe1\u5ea6\u5224\u5b9a\u3002\u800c\u6b63\u6001\u5206\u5e03\u4f5c\u4e3a\u5236\u9020\u8fc7\u7a0b\u6700\u5e38\u7528\u7684\u89e3\u6790\u6982\u7387\u6a21\u578b\uff0c\u5176\u533a\u95f4\u6982\u7387\u7684\u8ba1\u7b97\u662f\u7f6e\u4fe1\u533a\u95f4\u5e94\u7528\u7684\u6838\u5fc3\u5b9e\u64cd\u5185\u5bb9\uff0c\u53ef\u901a\u8fc7 z z <\/span><\/span>z<\/span><\/span><\/span><\/span><\/span>\u5206\u6570\u53d8\u6362\u7ed3\u5408\u67e5\u8868\u6cd5\u3001Excel\u3001Matlab\u7b49\u591a\u79cd\u5de5\u5177\u5b9e\u73b0\u7cbe\u51c6\u6c42\u89e3\u3002<\/p>\n

\u672c\u6587\u5c06\u7cfb\u7edf\u9610\u8ff0\u7f6e\u4fe1\u533a\u95f4\u7684\u6838\u5fc3\u5b9a\u4e49\u3001\u57fa\u4e8e\u6807\u51c6\u6b63\u6001\u5206\u5e03\u7684\u7ecf\u5178\u7f6e\u4fe1\u533a\u95f4\u7279\u5f81\uff0c\u540c\u65f6\u8be6\u7ec6\u4ecb\u7ecd\u6b63\u6001\u5206\u5e03\u533a\u95f4\u6982\u7387\u7684\u901a\u7528\u8ba1\u7b97\u65b9\u6cd5\u4e0e\u591a\u5de5\u5177\u5b9e\u64cd\u6d41\u7a0b\uff0c\u4e3a\u5236\u9020\u8fc7\u7a0b\u7684\u6982\u7387\u5316\u5206\u6790\u4e0e\u5de5\u7a0b\u51b3\u7b56\u63d0\u4f9b\u53ef\u843d\u5730\u7684\u65b9\u6cd5\u6846\u67b6\u3002<\/p>\n

1. \u7f6e\u4fe1\u533a\u95f4\u7684\u6838\u5fc3\u5b9a\u4e49\u4e0e\u7406\u8bba\u57fa\u7840<\/h3>\n

1.1 \u7f6e\u4fe1\u533a\u95f4\u7684\u672c\u8d28\u5185\u6db5<\/h4>\n

\u7f6e\u4fe1\u533a\u95f4\u662f\u5bf9\u8fde\u7eed\u578b\u968f\u673a\u8fc7\u7a0b\u53d6\u503c\u8303\u56f4\u4e0e\u5bf9\u5e94\u7f6e\u4fe1\u5ea6\u7684\u8054\u5408\u91cf\u5316\u63cf\u8ff0\uff0c\u5176\u6838\u5fc3\u662f\u57fa\u4e8e\u8fc7\u7a0b\u7684\u6bcd\u4f53\u6982\u7387\u5206\u5e03\u51fd\u6570\uff0c\u5b9a\u4e49\u4e00\u4e2a\u6570\u503c\u533a\u95f4\uff0c\u5e76\u8ba1\u7b97\u8fc7\u7a0b\u8f93\u51fa\u843d\u5165\u8be5\u533a\u95f4\u7684\u6982\u7387\uff0c\u8fd9\u4e2a\u6982\u7387\u5373\u4e3a\u7f6e\u4fe1\u5ea6\u3002\u7b80\u5355\u6765\u8bf4\uff0c\u7f6e\u4fe1\u533a\u95f4\u56de\u7b54\u4e86 \u201c\u57fa\u4e8e\u5f53\u524d\u7684\u6982\u7387\u5206\u5e03\u89c4\u5f8b\uff0c\u8fc7\u7a0b\u8f93\u51fa\u843d\u5728\u67d0\u4e00\u533a\u95f4\u5185\u7684\u53ef\u80fd\u6027\u6709\u591a\u5927\u201d \u8fd9\u4e00\u6838\u5fc3\u95ee\u9898\uff0c\u662f\u5c06\u89e3\u6790\u6982\u7387\u6a21\u578b\u8f6c\u5316\u4e3a\u5de5\u7a0b\u5b9e\u9645\u5e94\u7528\u7684\u5173\u952e\u6865\u6881\u3002<\/p>\n

\u4ece\u51e0\u4f55\u610f\u4e49\u4e0a\u770b\uff0c\u7f6e\u4fe1\u533a\u95f4\u7684\u7f6e\u4fe1\u5ea6\u7b49\u4ef7\u4e8e\u6982\u7387\u5206\u5e03\u51fd\u6570\u66f2\u7ebf\u5728\u8be5\u533a\u95f4\u5185\u4e0e\u6a2a\u8f74\u56f4\u6210\u7684\u9762\u79ef\u3002\u7531\u4e8e\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf\u53d6\u5355\u4e00\u6570\u503c\u7684\u6982\u7387\u4e3a0\uff0c\u56e0\u6b64\u6240\u6709\u7f6e\u4fe1\u533a\u95f4\u5747\u4e3a\u8fde\u7eed\u7684\u6570\u503c\u533a\u95f4\uff0c\u8fd9\u4e0e\u6982\u7387\u5206\u5e03\u51fd\u6570\u7684\u5206\u6790\u903b\u8f91\u4fdd\u6301\u4e00\u81f4\u3002<\/p>\n

1.2 \u7f6e\u4fe1\u533a\u95f4\u7684\u6838\u5fc3\u7406\u8bba\u57fa\u7840<\/h4>\n

\u7f6e\u4fe1\u533a\u95f4\u7684\u8ba1\u7b97\u4ee5\u8fc7\u7a0b\u7684\u5e73\u7a33\u968f\u673a\u8fc7\u7a0b\u5047\u8bbe\u548c\u5df2\u77e5\u6bcd\u4f53\u6982\u7387\u5206\u5e03\u4e3a\u524d\u63d0\uff1a<\/p>\n

  • \u8fc7\u7a0b\u4e3a\u5e73\u7a33\u968f\u673a\u8fc7\u7a0b\uff0c\u5176\u6982\u7387\u5206\u5e03\u51fd\u6570\u4e0d\u968f\u65f6\u95f4\u53d8\u5316\uff0c\u4fdd\u8bc1\u7f6e\u4fe1\u533a\u95f4\u7684\u7279\u5f81\u5728\u65f6\u95f4\u7ef4\u5ea6\u4e0a\u7a33\u5b9a\uff1b<\/li>\n
  • \u5df2\u77e5\u8fc7\u7a0b\u7684\u6bcd\u4f53\u6982\u7387\u5206\u5e03\uff08\u5982\u6b63\u6001\u5206\u5e03\u3001\u5747\u5300\u5206\u5e03\uff09\uff0c\u53ef\u901a\u8fc7\u5206\u5e03\u7684\u89e3\u6790\u516c\u5f0f\u8ba1\u7b97\u6307\u5b9a\u533a\u95f4\u7684\u9762\u79ef\uff0c\u5373\u7f6e\u4fe1\u5ea6\u3002<\/li>\n

    \u5728\u5236\u9020\u8fc7\u7a0b\u4e2d\uff0c\u7531\u4e8e\u7edd\u5927\u591a\u6570\u7eaf\u968f\u673a\u6548\u5e94\u5747\u670d\u4ece\u6b63\u6001\u5206\u5e03\uff0c\u56e0\u6b64\u57fa\u4e8e\u6b63\u6001\u5206\u5e03\u7684\u7f6e\u4fe1\u533a\u95f4\u6210\u4e3a\u5e94\u7528\u6700\u5e7f\u6cdb\u7684\u5f62\u5f0f\uff0c\u800c\u6807\u51c6\u6b63\u6001\u5206\u5e03\uff08 Z \u223c N ( 0 , 1 ) Z \\\\sim N(0,1) <\/span><\/span>Z<\/span><\/span>\u223c<\/span><\/span><\/span><\/span>N<\/span>(<\/span>0<\/span>,<\/span><\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span>\uff09\u56e0\u5f62\u5f0f\u7b80\u5316\uff0c\u6210\u4e3a\u7f6e\u4fe1\u533a\u95f4\u7279\u5f81\u5206\u6790\u7684\u57fa\u7840\u3002<\/p>\n

    2. \u6807\u51c6\u6b63\u6001\u5206\u5e03\u7684\u7ecf\u5178\u7f6e\u4fe1\u533a\u95f4\u4e0e\u6838\u5fc3\u7279\u5f81<\/h3>\n

    \u6807\u51c6\u6b63\u6001\u5206\u5e03\u662f\u5747\u503c \u03bc = 0 \\\\mu=0 <\/span><\/span>\u03bc<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u3001\u6807\u51c6\u5dee \u03c3 = 1 \\\\sigma=1 <\/span><\/span>\u03c3<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u7684\u6b63\u6001\u5206\u5e03\uff0c\u5176\u6982\u7387\u5206\u5e03\u51fd\u6570\u5177\u6709\u5b8c\u7f8e\u7684\u5bf9\u79f0\u6027\uff0c\u57fa\u4e8e\u6b64\u63a8\u5bfc\u7684 \u00b1 1 \u03c3 \\\\pm1\\\\sigma <\/span><\/span>\u00b1<\/span>1<\/span>\u03c3<\/span><\/span><\/span><\/span><\/span>\u3001 \u00b1 2 \u03c3 \\\\pm2\\\\sigma <\/span><\/span>\u00b1<\/span>2<\/span>\u03c3<\/span><\/span><\/span><\/span><\/span>\u3001 \u00b1 3 \u03c3 \\\\pm3\\\\sigma <\/span><\/span>\u00b1<\/span>3<\/span>\u03c3<\/span><\/span><\/span><\/span><\/span>\u7ecf\u5178\u7f6e\u4fe1\u533a\u95f4\uff0c\u662f\u5236\u9020\u8fc7\u7a0b\u7edf\u8ba1\u8fc7\u7a0b\u63a7\u5236\u7684\u6838\u5fc3\u7406\u8bba\u4f9d\u636e\u3002<\/p>\n

    2.1 \u7f6e\u4fe1\u533a\u95f4\u7684\u901a\u7528\u8ba1\u7b97\u65b9\u6cd5<\/h4>\n

    \u5bf9\u4e8e\u6807\u51c6\u6b63\u6001\u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf Z Z <\/span><\/span>Z<\/span><\/span><\/span><\/span><\/span>\uff0c\u5176\u5728\u533a\u95f4 [ z 1 , z 2 ] [z_1,z_2] <\/span><\/span>[<\/span>z<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>z<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span><\/span>\u5185\u7684\u7f6e\u4fe1\u5ea6\uff08\u6982\u7387\uff09\u8ba1\u7b97\u9075\u5faa\u7d2f\u79ef\u6982\u7387\u76f8\u51cf\u6cd5\uff0c\u5373\u901a\u8fc7\u8ba1\u7b97\u7d2f\u79ef\u6982\u7387\u51fd\u6570\u5728\u4e24\u4e2a\u533a\u95f4\u7aef\u70b9\u7684\u5dee\u503c\uff0c\u5f97\u5230\u533a\u95f4\u5185\u7684\u9762\u79ef\uff0c\u516c\u5f0f\u4e3a\uff1a P ( z 1 < Z < z 2 ) = \u03a6 ( z 2 ) \u2212 \u03a6 ( z 1 ) P(z_1 < Z < z_2) = \\\\Phi(z_2) – \\\\Phi(z_1) <\/span><\/span>P<\/span>(<\/span>z<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><<\/span><\/span><\/span><\/span>Z<\/span><\/span><<\/span><\/span><\/span><\/span>z<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>\u03a6<\/span>(<\/span>z<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>\u03a6<\/span>(<\/span>z<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span> \u5176\u4e2d\uff0c \u03a6 ( z ) \\\\Phi(z) <\/span><\/span>\u03a6<\/span>(<\/span>z<\/span>)<\/span><\/span><\/span><\/span><\/span>\u4e3a\u6807\u51c6\u6b63\u6001\u5206\u5e03\u7684\u7d2f\u79ef\u6982\u7387\u51fd\u6570\uff0c\u8868\u5f81 Z Z <\/span><\/span>Z<\/span><\/span><\/span><\/span><\/span>\u53d6\u503c\u5c0f\u4e8e z z <\/span><\/span>z<\/span><\/span><\/span><\/span><\/span>\u7684\u6982\u7387\u3002<\/p>\n

    \u5229\u7528\u8fd9\u4e00\u65b9\u6cd5\uff0c\u53ef\u5206\u522b\u8ba1\u7b97 \u00b1 1 \u03c3 \\\\pm1\\\\sigma <\/span><\/span>\u00b1<\/span>1<\/span>\u03c3<\/span><\/span><\/span><\/span><\/span>\u3001 \u00b1 2 \u03c3 \\\\pm2\\\\sigma <\/span><\/span>\u00b1<\/span>2<\/span>\u03c3<\/span><\/span><\/span><\/span><\/span>\u3001 \u00b1 3 \u03c3 \\\\pm3\\\\sigma <\/span><\/span>\u00b1<\/span>3<\/span>\u03c3<\/span><\/span><\/span><\/span><\/span>\u533a\u95f4\u7684\u7f6e\u4fe1\u5ea6\uff0c\u5f97\u5230\u5236\u9020\u5de5\u7a0b\u4e2d\u6700\u5e38\u7528\u7684\u4e09\u7ec4\u7ecf\u5178\u7f6e\u4fe1\u533a\u95f4\u7279\u5f81\u3002<\/p>\n

    2.2 \u6807\u51c6\u6b63\u6001\u5206\u5e03\u7684\u4e09\u7ec4\u7ecf\u5178\u7f6e\u4fe1\u533a\u95f4<\/h4>\n

    \u901a\u8fc7\u7d2f\u79ef\u6982\u7387\u76f8\u51cf\u6cd5\u7ed3\u5408\u6807\u51c6\u6b63\u6001\u5206\u5e03\u8868\u67e5\u8be2\uff0c\u53ef\u7cbe\u51c6\u6c42\u89e3\u4e09\u7ec4\u6838\u5fc3\u533a\u95f4\u7684\u7f6e\u4fe1\u5ea6\uff0c\u5176\u7ed3\u679c\u6210\u4e3a\u5236\u9020\u8fc7\u7a0b\u8d28\u91cf\u5224\u5b9a\u4e0e\u63a7\u5236\u9650\u8bbe\u5b9a\u7684\u901a\u7528\u51c6\u5219\uff1a<\/p>\n

  • \u00b1 1 \u03c3 \\\\boldsymbol{\\\\pm1\\\\sigma} <\/span><\/span>\u00b1<\/span>1<\/span>\u03c3<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7f6e\u4fe1\u533a\u95f4\uff1a P ( \u2212 1 < Z < 1 ) = \u03a6 ( 1 ) \u2212 \u03a6 ( \u2212 1 ) = 0.841 \u2212 0.159 = 0.682 P(-1 < Z < 1) = \\\\Phi(1) – \\\\Phi(-1) = 0.841 – 0.159 = 0.682 <\/span><\/span>P<\/span>(<\/span>\u2212<\/span>1<\/span><\/span><<\/span><\/span><\/span><\/span>Z<\/span><\/span><<\/span><\/span><\/span><\/span>1<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>\u03a6<\/span>(<\/span>1<\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>\u03a6<\/span>(<\/span>\u2212<\/span>1<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>0.841<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>0.159<\/span><\/span>=<\/span><\/span><\/span><\/span>0.682<\/span><\/span><\/span><\/span><\/span>\uff0c\u537368.2%\u7684\u7f6e\u4fe1\u5ea6\uff0c\u8fc7\u7a0b\u8f93\u51fa\u670968.2%\u7684\u53ef\u80fd\u6027\u843d\u5728\u5747\u503c\u5de6\u53f31\u4e2a\u6807\u51c6\u5dee\u8303\u56f4\u5185\uff1b<\/li>\n
  • \u00b1 2 \u03c3 \\\\boldsymbol{\\\\pm2\\\\sigma} <\/span><\/span>\u00b1<\/span>2<\/span>\u03c3<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7f6e\u4fe1\u533a\u95f4\uff1a P ( \u2212 2 < Z < 2 ) = \u03a6 ( 2 ) \u2212 \u03a6 ( \u2212 2 ) \u2248 0.977 \u2212 0.023 = 0.954 P(-2 < Z < 2) = \\\\Phi(2) – \\\\Phi(-2) \\\\approx 0.977 – 0.023 = 0.954 <\/span><\/span>P<\/span>(<\/span>\u2212<\/span>2<\/span><\/span><<\/span><\/span><\/span><\/span>Z<\/span><\/span><<\/span><\/span><\/span><\/span>2<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>\u03a6<\/span>(<\/span>2<\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>\u03a6<\/span>(<\/span>\u2212<\/span>2<\/span>)<\/span><\/span>\u2248<\/span><\/span><\/span><\/span>0.977<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n","protected":false},"excerpt":{"rendered":"

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