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概率论与数理统计
附表：正态/t/F等分布表
附录5：卡方分布表
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附录5：卡方分布表
<table class=layui-table><thead><tr><th >n\a</th><th >0.001</th><th >0.005</th><th >0.01</th><th >0.025</th><th >0.05</th><th >0.10</th><th >0.25</th><th >0.50</th><th >0.75</th><th >0.90</th><th >0.95</th><th >0.975</th><th >0.99</th><th >0.995</th></tr></thead><tbody><tr><td >1</td><td >10,828</td><td >7,879</td><td >6,635</td><td >5,024</td><td >3,841</td><td >2,706</td><td >1,323</td><td >0.455</td><td >0.102</td><td >0.016</td><td >0.004</td><td >0.001</td><td >0.000</td><td >0.000</td></tr><tr><td >2</td><td >13,816</td><td >10,597</td><td >9,210</td><td >7,378</td><td >5,991</td><td >4,605</td><td >2,773</td><td >1,386</td><td >0.575</td><td >0.211</td><td >0.103</td><td >0.051</td><td >0.020</td><td >0.010</td></tr><tr><td >3</td><td >16,266</td><td >12,838</td><td >11,345</td><td >9,348</td><td >7,815</td><td >6,251</td><td >4,108</td><td >2,366</td><td >1,213</td><td >0.584</td><td >0.352</td><td >0.216</td><td >0.115</td><td >0.072</td></tr><tr><td >4</td><td >18,467</td><td >14,860</td><td >13,277</td><td >11,143</td><td >9,488</td><td >7,779</td><td >5,385</td><td >3,357 </td><td >1,923</td><td >1,064</td><td >0.711</td><td >0.484</td><td >0.297</td><td >0.207</td></tr><tr><td >5</td><td >20,515</td><td >16,750</td><td >15,086</td><td >12,833</td><td >11,070</td><td >9,236</td><td >6,626</td><td >4,351</td><td >2,675</td><td >1,610</td><td >1,145</td><td >0.831</td><td >0.554</td><td >0.412</td></tr><tr><td >6</td><td >22,458</td><td >18,548</td><td >16,812</td><td >14,449</td><td >12,592</td><td >10,645</td><td >7,841</td><td >5,348</td><td >3,455</td><td >2,204 </td><td >1,635</td><td >1,237</td><td >0.872</td><td >0.676</td></tr><tr><td >7</td><td >24,322</td><td >20,278</td><td >18,475</td><td >16,013</td><td >14,067</td><td >12,017</td><td >9,037</td><td >6,346</td><td >4,255</td><td >2,833</td><td >2,167</td><td >1,690</td><td >1,239</td><td >0.989</td></tr><tr><td >8</td><td >26,124</td><td >21,955</td><td >20,090</td><td >17,535</td><td >15,507</td><td >13,362</td><td >10,219</td><td >7,344</td><td >5,071</td><td >3,490</td><td >2,733</td><td >2,180</td><td >1,646</td><td >1,344</td></tr><tr><td >9</td><td >27,877</td><td >23,589</td><td >21,666</td><td >19,023</td><td >16,919</td><td >14,684</td><td >11,389</td><td >8,343</td><td >5,899</td><td >4,168</td><td >3,325</td><td >2,700</td><td >2,088</td><td >1,735</td></tr><tr><td >十</td><td >29,588</td><td >25,188</td><td >23,209</td><td >20,483</td><td >18,307</td><td >15,987</td><td >12,549</td><td >9,342</td><td >6,737</td><td >4,865</td><td >3,940 </td><td >3,247</td><td >2,558</td><td >2,156</td></tr><tr><td >十一</td><td >31,264</td><td >26,757</td><td >24,725</td><td >21,920</td><td >19,675</td><td >17,275</td><td >13,701</td><td >10,341</td><td >7,584</td><td >5,578</td><td >4,575</td><td >3,816</td><td >3,053 </td><td >2,603 </td></tr><tr><td >12</td><td >32,909</td><td >28,300</td><td >26,217</td><td >23,337</td><td >21,026</td><td >18,549</td><td >14,845</td><td >11,340</td><td >8,438</td><td >6,304</td><td >5,226</td><td >4,404</td><td >3,571</td><td >3,074</td></tr><tr><td >13</td><td >34,528</td><td >29,819</td><td >27,688</td><td >24,736</td><td >22,362</td><td >19,812</td><td >15,984</td><td >12,340</td><td >9,299</td><td >7,042</td><td >5,892</td><td >5,009 </td><td >4,107</td><td >3,565</td></tr><tr><td >14</td><td >36,123</td><td >31,319</td><td >29,141</td><td >26,119</td><td >23,685</td><td >21,064</td><td >17,117</td><td >13,339</td><td >10,165</td><td >7,790</td><td >6,571</td><td >5,629</td><td >4,660</td><td >4,075</td></tr><tr><td >十五</td><td >37,697</td><td >32,801</td><td >30,578</td><td >27,488</td><td >24,996</td><td >22,307</td><td >18,245</td><td >14,339</td><td >11,037</td><td >8,547</td><td >7,261</td><td >6,262</td><td >5,229</td><td >4,601</td></tr><tr><td >16</td><td >39,252</td><td >34,267</td><td >32,000</td><td >28,845</td><td >26,296</td><td >23,542</td><td >19,369</td><td >15,338</td><td >11,912</td><td >9,312</td><td >7,962</td><td >6,908</td><td >5,812</td><td >5,142</td></tr><tr><td >17 号</td><td >40,790</td><td >35,718</td><td >33,409</td><td >30,191</td><td >27,587</td><td >24,769</td><td >20,489</td><td >16,338</td><td >12,792</td><td >10,085</td><td >8,672</td><td >7,564</td><td >6,408</td><td >5,697</td></tr><tr><td >18</td><td >42,312</td><td >37,156</td><td >34,805</td><td >31,526</td><td >28,869</td><td >25,989</td><td >21,605</td><td >17,338</td><td >13,675</td><td >10,865</td><td >9,390</td><td >8,231</td><td >7,015</td><td >6,265</td></tr><tr><td >19</td><td >43,820</td><td >38,582</td><td >36,191</td><td >32,852</td><td >30,144</td><td >27,204</td><td >22,718</td><td >18,338</td><td >14,562</td><td >11,651</td><td >10,117</td><td >8,907</td><td >7,633</td><td >6,844</td></tr><tr><td >二十</td><td >45,315</td><td >39,997</td><td >37,566</td><td >34,170</td><td >31,410</td><td >28,412</td><td >23,828</td><td >19,337</td><td >15,452</td><td >12,443</td><td >10,851</td><td >9,591</td><td >8,260</td><td >7,434</td></tr><tr><td >21</td><td >46,797</td><td >41,401</td><td >38,932</td><td >35,479</td><td >32,671</td><td >29,615</td><td >24,935</td><td >20,337</td><td >16,344</td><td >13,240</td><td >11,591</td><td >10,283</td><td >8,897</td><td >8,034</td></tr><tr><td >22</td><td >48,268</td><td >42,796</td><td >40,289</td><td >36,781</td><td >33,924</td><td >30,813</td><td >26,039</td><td >21,337</td><td >17,240</td><td >14,041</td><td >12,338</td><td >10,982</td><td >9,542</td><td >8,643</td></tr><tr><td >23</td><td >49,728</td><td >44,181</td><td >41,638</td><td >38,076</td><td >35,172</td><td >32,007</td><td >27,141</td><td >22,337</td><td >18,137</td><td >14,848</td><td >13,091</td><td >11,689</td><td >10,196</td><td >9,260</td></tr><tr><td >24</td><td >51,179</td><td >45,559</td><td >42,980</td><td >39,364</td><td >36,415</td><td >33,196</td><td >28,241</td><td >23,337</td><td >19,037</td><td >15,659</td><td >13,848</td><td >12,401</td><td >10,856</td><td >9,886</td></tr><tr><td >25</td><td >52,620</td><td >46,928</td><td >44,314</td><td >40,646</td><td >37,652</td><td >34,382</td><td >29,339</td><td >24,337</td><td >19,939</td><td >16,473</td><td >14,611</td><td >13,120</td><td >11,524</td><td >10,520</td></tr><tr><td >26</td><td >54,052</td><td >48,290</td><td >45,642</td><td >41,923</td><td >38,885</td><td >35,563</td><td >30,435</td><td >25,336</td><td >20,843</td><td >17,292</td><td >15,379</td><td >13,844</td><td >12,198</td><td >11,160</td></tr><tr><td >27</td><td >55,476</td><td >49,645</td><td >46,963</td><td >43,195</td><td >40,113</td><td >36,741</td><td >31,528</td><td >26,336</td><td >21,749</td><td >18,114</td><td >16,151</td><td >14,573</td><td >12,879</td><td >11,808</td></tr><tr><td >28</td><td >56,892</td><td >50,993</td><td >48,278</td><td >44,461</td><td >41,337</td><td >37,916</td><td >32,620</td><td >27,336</td><td >22,657</td><td >18,939</td><td >16,928</td><td >15,308</td><td >13,565</td><td >12,461</td></tr><tr><td >29</td><td >58,301</td><td >52,336</td><td >49,588</td><td >45,722</td><td >42,557</td><td >39,087</td><td >33,711</td><td >28,336</td><td >23,567</td><td >19,768</td><td >17,708</td><td >16,047</td><td >14,256</td><td >13,121</td></tr><tr><td >30</td><td >59,703</td><td >53,672</td><td >50,892</td><td >46,979</td><td >43,773</td><td >40,256</td><td >34,800</td><td >29,336</td><td >24,478</td><td >20,599</td><td >18,493</td><td >16,791</td><td >14,953</td><td >13,787</td></tr><tr><td >35</td><td >66,619</td><td >60,275</td><td >57,342</td><td >53,203</td><td >49,802</td><td >46,059</td><td >40,223</td><td >34,336</td><td >29,054</td><td >24,797</td><td >22,465</td><td >20,569</td><td >18,509</td><td >17,192</td></tr><tr><td >40</td><td >73,402</td><td >66,766</td><td >63,691</td><td >59,342</td><td >55,758</td><td >51,805</td><td >45,616</td><td >39,335</td><td >33,660</td><td >29,051</td><td >26,509</td><td >24,433</td><td >22,164</td><td >20,707</td></tr><tr><td >四五</td><td >80,078</td><td >73,166</td><td >69,957</td><td >65,410</td><td >61,656</td><td >57,505</td><td >50,985</td><td >44,335</td><td >38,291</td><td >33,350</td><td >30,612</td><td >28,366</td><td >25,901</td><td >24,311</td></tr><tr><td >五十</td><td >86,660</td><td >79,450</td><td >76,154</td><td >71,420</td><td >67,505</td><td >63,167</td><td >56,334</td><td >49,335</td><td >42,942</td><td >37,689</td><td >34,764</td><td >32,357</td><td >29,707</td><td >27,991</td></tr><tr><td >60</td><td >99,607</td><td >91,952</td><td >88,379</td><td >83,298</td><td >79,082</td><td >74,397</td><td >66,981</td><td >59,335</td><td >52,294</td><td >46,459</td><td >43,188</td><td >40,482</td><td >37,485</td><td >35,534</td></tr><tr><td >70</td><td >112,317</td><td >104215</td><td >100425</td><td >95,023</td><td >90,531</td><td >85,527</td><td >77,577</td><td >69,335</td><td >61,698</td><td >55,329</td><td >51,739</td><td >48,758</td><td >45,442</td><td >43,275</td></tr><tr><td >80</td><td >124,839</td><td >116,321</td><td >112,329</td><td >106,629</td><td >101,879</td><td >96,578</td><td >88130</td><td >79,334</td><td >71,145</td><td >64,278</td><td >60,391</td><td >57,153</td><td >53,540</td><td >51,172</td></tr><tr><td >90</td><td >137208</td><td >128,299</td><td >124 116</td><td >118 136</td><td >113 145</td><td >107,565</td><td >98,650</td><td >89,334</td><td >80,625</td><td >73,291</td><td >69,126</td><td >65,647</td><td >61,754</td><td >59,196</td></tr><tr><td >100</td><td >149,449</td><td >140 169</td><td >135,807</td><td >129,561</td><td >124,342</td><td >118,498</td><td >109141</td><td >99,334</td><td >90133</td><td >82,358</td><td >77,929</td><td >74,222</td><td >70,065</td><td >67,328</td></tr></tbody></table> 要理解上a分位数与下a分位数 这其中的区别还是需要一点小常识。 总体来说，全国各大高校统计真题分为五大门派：纯贾、贾茆、纯茆、贾Pro、茆Pro。这里的贾不仅仅指贾俊平的《统计学》，而是以贾俊平《统计学》为代表的偏文、偏经济的一类教材，比如袁卫的《统计学》等。 同样，这里的茆不仅仅只是茆诗松的《概率论与数理统计》，而是以茆诗松《概率论与数理统计》为代表的偏数理的一类教材，比如盛骤的《概率论与数理统计》等。 他们给的表并不一样，要用1-a，详见 https://kb.kmath.cn/kbase/detail.aspx?id=1567
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附录4：标准正态分位数表
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附录6：卡方分布表2
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