2022年秋高中數(shù)學(xué)第七章隨機(jī)變量及其分布測(cè)評(píng)試題新人教A版選擇性必修第三冊(cè)

歡迎閱讀本文檔，希望本文檔能對(duì)您有所幫助！/r/n歡迎閱讀本文檔，希望本文檔能對(duì)您有所幫助！/r/n歡迎閱讀本文檔，希望本文檔能對(duì)您有所幫助！/r/n歡迎閱讀本文檔，希望本文檔能對(duì)您有所幫助！/r/n歡迎閱讀本文檔，希望本文檔能對(duì)您有所幫助！/r/n歡迎閱讀本文檔，希望本文檔能對(duì)您有所幫助！/r/n第七章測(cè)評(píng)/r/n一、選擇題/r/n:/r/n本題共/r/n8/r/n小題/r/n,/r/n每小題/r/n5/r/n分/r/n,/r/n共/r/n40/r/n分/r/n./r/n在每小題給出的四個(gè)選項(xiàng)中/r/n,/r/n只有一項(xiàng)是符合題目要求的/r/n./r/n1/r/n./r/n下列說(shuō)法不正確的是(/r/n/r/n)/r/nA/r/n./r/n某輛汽車(chē)一年中發(fā)生事故的次數(shù)是一個(gè)離散型隨機(jī)變量/r/nB/r/n./r/n正態(tài)分布隨機(jī)變量等于一個(gè)特定實(shí)數(shù)的概率為0/r/nC/r/n./r/n公式/r/nE/r/n(/r/nX/r/n)/r/n=np/r/n可以用來(lái)計(jì)算所有離散型隨機(jī)變量的均值/r/nD/r/n./r/n從一副撲克牌中隨機(jī)抽取5張,其中梅花的張數(shù)服從超幾何分布/r/n2/r/n./r/n若/r/nX/r/n的分布列為/r/nX/r/n0/r/n1/r/nP/r/n1/r/na/r/n則/r/nE/r/n(/r/nX/r/n)/r/n=/r/n(/r/n/r/n)/r/nA/r/n./r/n4/r/n5/r/n /r/nB/r/n./r/n1/r/nC/r/n./r/n2/r/n5/r/n /r/nD/r/n./r/n3/r/n./r/n如果隨機(jī)變量/r/nX~N/r/n(4,1),則/r/nP/r/n(/r/nX/r/n≤/r/n2)/r/n=/r/n(/r/n/r/n)/r/n(注:/r/nP/r/n(/r/nμ/r/n-/r/n2/r/nσ/r/n≤/r/nX/r/n≤/r/nμ/r/n+/r/n2/r/nσ/r/n)/r/n≈/r/n0/r/n./r/n9545)/r/nA/r/n./r/n0/r/n./r/n210/r/n /r/nB/r/n./r/n0/r/n./r/n02275/r/nC/r/n./r/n0/r/n./r/n0456/r/n /r/nD/r/n./r/n0/r/n./r/n0215/r/n4/r/n./r/n下列隨機(jī)變量/r/nX/r/n中,不服從超幾何分布的是(/r/n/r/n)/r/nA/r/n./r/n在含有4件次品的15件產(chǎn)品中,任取3件,其中正品數(shù)和次品數(shù)的差為/r/nX/r/nB/r/n./r/n在6個(gè)黑球和3個(gè)白球中,任取4個(gè)球,其中黑球的個(gè)數(shù)為/r/nX/r/nC/r/n./r/n在20個(gè)乒乓球中,有12個(gè)正品和8個(gè)次品,從中任取4個(gè),其中次品的個(gè)數(shù)為/r/nX/r/nD/r/n./r/n從24名男生和16名女生中,任選10名學(xué)生,其中女生的人數(shù)為/r/nX/r/n5/r/n./r/n對(duì)標(biāo)有不同編號(hào)的6件正品和4件次品的產(chǎn)品進(jìn)行檢測(cè),不放回地依次摸出2件/r/n./r/n在第一次摸到正品的條件下,第二次也摸到正品的概率是(/r/n/r/n)/r/nA/r/n./r/n3/r/n5/r/n /r/nB/r/n./r/n2/r/n5/r/n /r/nC/r/n./r/n1/r/n10/r/n /r/n6/r/n./r/n設(shè)隨機(jī)變量/r/nX~B/r/n(2,/r/np/r/n),隨機(jī)變量/r/nY~B/r/n(3,/r/np/r/n),若/r/nP/r/n(/r/nX/r/n≥/r/n1)/r/n=/r/n5/r/n9/r/n,則/r/nD/r/n(3/r/nY+/r/n1)/r/n=/r/n(/r/n/r/nA/r/n./r/n2/r/n /r/nB/r/n./r/n3/r/n /r/nC/r/n./r/n6/r/n /r/nD/r/n./r/n7/r/n7/r/n./r/n投籃測(cè)試中,每人投5次,至少投中2次才能通過(guò)測(cè)試/r/n./r/n已知某同學(xué)每次投籃投中的概率為0/r/n./r/n8,且各次投籃是否投中相互獨(dú)立,則該同學(xué)未通過(guò)測(cè)試的概率為(/r/n/r/n)/r/nA/r/n./r/n0/r/n./r/n00672/r/n /r/nB/r/n./r/n0/r/n./r/n00096/r/n /r/nC/r/n./r/n0/r/n./r/n00064/r/n /r/nD/r/n./r/n0/r/n./r/n00032/r/n8/r/n./r/n9粒種子分種在3個(gè)坑內(nèi),每個(gè)坑3粒,每粒種子發(fā)芽的概率為0/r/n./r/n5/r/n./r/n若一個(gè)坑內(nèi)至少有1粒種子發(fā)芽,則這個(gè)坑不需要補(bǔ)種;若一個(gè)坑內(nèi)的種子都沒(méi)發(fā)芽,則這個(gè)坑需要補(bǔ)種/r/n./r/n假定每個(gè)坑至多補(bǔ)種一次,每補(bǔ)種1個(gè)坑需10元,用隨機(jī)變量/r/nX/r/n表示補(bǔ)種費(fèi)用,則/r/nX/r/n的均值等于(/r/n/r/n)/r/nA/r/n./r/n15/r/n4/r/n /r/nB/r/n./r/n15/r/n8/r/n /r/nC/r/n./r/n3/r/n8/r/n /r/n二、選擇題/r/n:/r/n本題共/r/n4/r/n小題/r/n,/r/n每小題/r/n5/r/n分/r/n,/r/n共/r/n20/r/n分/r/n./r/n在每小題給出的選項(xiàng)中/r/n,/r/n有多項(xiàng)符合題目要求/r/n./r/n全部選對(duì)的得/r/n5/r/n分/r/n,/r/n部分選對(duì)的得/r/n2/r/n分/r/n,/r/n有選錯(cuò)的得/r/n0/r/n分/r/n./r/n9/r/n./r/n(2022/r/n遼寧沈陽(yáng)一模/r/n)某市教育局為了解雙減政策的落實(shí)情況,隨機(jī)在本市內(nèi)抽取了A,B兩所初級(jí)中學(xué),在每一所學(xué)校中各隨機(jī)抽取了200名學(xué)生,調(diào)查了他們課下做作業(yè)的時(shí)間,并根據(jù)調(diào)查結(jié)果繪制了如下頻率分布直方圖:/r/n由直方圖判斷,以下說(shuō)法正確的是(/r/n/r/n)/r/nA/r/n./r/n總體看,A校學(xué)生做作業(yè)平均時(shí)長(zhǎng)小于B校學(xué)生做作業(yè)平均時(shí)長(zhǎng)/r/nB/r/n./r/nB校所有學(xué)生做作業(yè)時(shí)長(zhǎng)都要大于A校學(xué)生做作業(yè)時(shí)長(zhǎng)/r/nC/r/n./r/nA校學(xué)生做作業(yè)時(shí)長(zhǎng)的中位數(shù)大于B校學(xué)生做作業(yè)的中位數(shù)/r/nD/r/n./r/nB校學(xué)生做作業(yè)時(shí)長(zhǎng)分布更接近正態(tài)分布/r/n10/r/n./r/n甲罐中有3個(gè)紅球、2個(gè)黑球,乙罐中有2個(gè)紅球、2個(gè)黑球,先從甲罐中隨機(jī)取出一球放入乙罐,以/r/nA/r/n表示事件/r/n“/r/n由甲罐取出的球是紅球/r/n”/r/n,再?gòu)囊夜拗须S機(jī)取出一球,以/r/nB/r/n表示事件/r/n“/r/n由乙罐取出的球是紅球/r/n”/r/n,則(/r/n/r/n)/r/nA/r/n./r/nP/r/n(/r/nA/r/n)/r/n=/r/n3/r/n5/r/n /r/nB/r/n./r/nP/r/n(/r/nB|A/r/n)/r/n=/r/nC/r/n./r/nP/r/n(/r/nB/r/n)/r/n=/r/n13/r/n25/r/n /r/nD/r/n./r/nP/r/n(/r/nA|B/r/n)/r/n=/r/n11/r/n./r/n(2022/r/n江蘇南京鼓樓校級(jí)月考/r/n)從裝有大小相同的3個(gè)白球和/r/nm/r/n個(gè)黑球的布袋中隨機(jī)摸取一個(gè)球,有放回地摸取5次,設(shè)摸到白球個(gè)數(shù)為/r/nX/r/n,已知/r/nE/r/n(/r/nX/r/n)/r/n=/r/n3,則下列說(shuō)法正確的是(/r/n/r/n)/r/nA/r/n./r/nD/r/n(/r/nX/r/n)/r/n=/r/n8/r/n5/r/n /r/nB/r/n./r/nD/r/n(/r/nX/r/n)/r/n=/r/n6/r/nC/r/n./r/nm=/r/n2/r/n /r/nD/r/n./r/nm=/r/n4/r/n12/r/n./r/n擲一個(gè)不均勻的硬幣6次,每次擲出正面的概率均為/r/n2/r/n3/r/n,恰好出現(xiàn)/r/nk/r/n次正面的概率記為/r/nP/r/nk/r/n,則下列說(shuō)法正確的是(/r/n/r/nA/r/n./r/nP/r/n1/r/n=P/r/n5/r/n /r/nB/r/n./r/nP/r/n1/r/n<P/r/n5/r/nC/r/n./r/n∑/r/nk/r/n=1/r/n6/r/nP/r/nk/r/nD/r/n./r/nP/r/n0/r/n,/r/nP/r/n1/r/n,/r/nP/r/n2/r/n,…,/r/nP/r/n6/r/n中最大值為/r/nP/r/n4/r/n三、填空題/r/n:/r/n本題共/r/n4/r/n小題/r/n,/r/n每小題/r/n5/r/n分/r/n,/r/n共/r/n20/r/n分/r/n./r/n13/r/n./r/n某市有/r/nm/r/n名男教師和/r/nn/r/n名女教師(/r/nm>n/r/n),從中任取兩名教師去西部支教,甲被抽中的概率為/r/n2/r/n9/r/n,一名男教師和一名女教師被抽中的概率為/r/n5/r/n9/r/n,則/r/nm/r/nn/r/n=/r/n/r/n,記去支教的教師中男教師的人數(shù)是/r/nξ/r/n,則/r/nE/r/n(/r/nξ/r/n)/r/n=/r/n14/r/n./r/n(2022/r/n黑龍江齊齊哈爾一模/r/n)橘生淮南則為橘,生于淮北則為枳,出自《屢子使楚》/r/n./r/n意思是說(shuō),橘樹(shù)生長(zhǎng)在淮河以南的地方就是橘樹(shù),生長(zhǎng)在淮河以北的地方就是枳樹(shù),現(xiàn)在常用來(lái)比喻一旦環(huán)境改變,事物的性質(zhì)也可能隨之改變/r/n./r/n某科研院校培育橘樹(shù)新品種,使得橘樹(shù)在淮北種植成功,經(jīng)過(guò)科學(xué)統(tǒng)計(jì),單個(gè)果品的質(zhì)量/r/nξ/r/n(單位:g)近似服從正態(tài)分布/r/nN/r/n(90,/r/nσ/r/n2/r/n),且/r/nP/r/n(86/r/n</r/nξ/r/n≤/r/n90)/r/n=/r/n0/r/n./r/n2,在有1000個(gè)的一批橘果中,估計(jì)單個(gè)果品質(zhì)量不低于94g的橘果個(gè)數(shù)為/r/n/r/n./r/n

/r/n15/r/n./r/n甲罐中有5個(gè)紅球、2個(gè)白球和3個(gè)黑球,乙罐中有4個(gè)紅球、3個(gè)白球和3個(gè)黑球,先從甲罐中隨機(jī)取出一球放入乙罐,分別以/r/nA/r/n1/r/n,/r/nA/r/n2/r/n和/r/nA/r/n3/r/n表示由甲罐中取出的球是紅球、白球和黑球的事件;再?gòu)囊夜拗须S機(jī)取出一球,以/r/nB/r/n表示由乙罐中取出的球是紅球的事件/r/n./r/n則/r/nP/r/n(/r/nB/r/n)/r/n=/r/n/r/n./r/n

/r/n16/r/n./r/n(2022/r/n浙江模擬/r/n)某學(xué)校組織教師進(jìn)行/r/n“/r/n學(xué)習(xí)強(qiáng)國(guó)/r/n”/r/n知識(shí)競(jìng)賽,規(guī)則為:每位參賽教師都要回答3個(gè)問(wèn)題,且這三個(gè)問(wèn)題回答正確與否相互之間不影響,已知對(duì)給出的3個(gè)問(wèn)題,教師甲答對(duì)的概率分別為/r/n3/r/n4/r/n,/r/n1/r/n2/r/n,/r/np/r/n./r/n若教師甲恰好答對(duì)3個(gè)問(wèn)題的概率是/r/n1/r/n4/r/n,則/r/np=/r/n/r/n,在前述條件下,設(shè)隨機(jī)變量/r/nX/r/n表示教師甲答對(duì)題目的個(gè)數(shù),則/r/n四、解答題/r/n:/r/n本題共/r/n6/r/n小題/r/n,/r/n共/r/n70/r/n分/r/n./r/n解答應(yīng)寫(xiě)出文字說(shuō)明、證明過(guò)程或演算步驟/r/n./r/n17/r/n./r/n(10/r/n分/r/n)/r/n一家面包房根據(jù)以往某種面包的銷(xiāo)售記錄,繪制了日銷(xiāo)售量的頻率分布直方圖,如圖所示/r/n./r/n將日銷(xiāo)售量落入各組的頻率視為概率,并假設(shè)每天的銷(xiāo)售量相互獨(dú)立/r/n./r/n(1)求在未來(lái)連續(xù)3天里,有連續(xù)2天的日銷(xiāo)售量都不低于100個(gè)且另1天的日銷(xiāo)售量低于50個(gè)的概率;/r/n(2)用/r/nX/r/n表示在未來(lái)3天里日銷(xiāo)售量不低于100個(gè)的天數(shù),求隨機(jī)變量/r/nX/r/n的分布列,均值及方差/r/n./r/n18/r/n./r/n(12/r/n分/r/n)在某次數(shù)學(xué)考試中,考生的成績(jī)/r/nξ/r/n服從一個(gè)正態(tài)分布,即/r/nξ/r/n~N/r/n(90,100)/r/n./r/n(1)試求考試成績(jī)/r/nξ/r/n位于區(qū)間[70,110]上的概率;/r/n(2)若這次考試共有2000名考生,試估計(jì)考試成績(jī)?cè)赱80,100]的考生大約有多少人?/r/n19/r/n./r/n(12/r/n分/r/n)某校從學(xué)生會(huì)宣傳部6名成員(其中男生4人,女生2人)中,任選3人參加某省舉辦的演講比賽活動(dòng)/r/n./r/n(1)設(shè)所選3人中女生人數(shù)為/r/nX/r/n,求/r/nX/r/n的分布列;/r/n(2)求男生甲或女生乙被選中的概率;/r/n(3)設(shè)/r/n“/r/n男生甲被選中/r/n”/r/n為事件/r/nA/r/n,/r/n“/r/n女生乙被選中/r/n”/r/n為事件/r/nB/r/n,求/r/nP/r/n(/r/nB/r/n)和/r/nP/r/n(/r/nB|A/r/n)/r/n./r/n20/r/n./r/n(12/r/n分/r/n)一盒中裝有9張各寫(xiě)有一個(gè)數(shù)字的卡片,其中4張卡片上的數(shù)字是1,3張卡片上的數(shù)字是2,2張卡片上的數(shù)字是3/r/n./r/n從盒中任取3張卡片/r/n./r/n(1)求所取3張卡片上的數(shù)字完全相同的概率;/r/n(2)/r/nX/r/n表示所取3張卡片上的數(shù)字的中位數(shù),求/r/nX/r/n的分布列與數(shù)學(xué)期望/r/n./r/n(注:若三個(gè)數(shù)/r/na/r/n,/r/nb/r/n,/r/nc/r/n滿足/r/na/r/n≤/r/nb/r/n≤/r/nc/r/n,則稱(chēng)/r/nb/r/n為這三個(gè)數(shù)的中位數(shù))/r/n21/r/n./r/n(12/r/n分/r/n)/r/n“/r/n十一黃金周/r/n”/r/n期間三亞景區(qū)迎來(lái)了游客高峰期/r/n./r/n游客小李從/r/n“/r/n大小洞天/r/n”/r/n景區(qū)到/r/n“/r/n天涯海角/r/n”/r/n景區(qū)有/r/nL/r/n1/r/n,/r/nL/r/n2/r/n兩條路線(如圖),路線/r/nL/r/n1/r/n上有/r/nA/r/n1/r/n,/r/nA/r/n2/r/n,/r/nA/r/n3/r/n三個(gè)風(fēng)景點(diǎn),各風(fēng)景點(diǎn)遇到堵塞的概率均為/r/n2/r/n3/r/n;/r/nL/r/n2/r/n路線上有/r/nB/r/n1/r/n,/r/nB/r/n2/r/n兩個(gè)風(fēng)景點(diǎn),各風(fēng)景點(diǎn)遇到堵塞的概率依次為/r/n3/r/n(1)若走/r/nL/r/n1/r/n路線,求最多遇到1次堵塞的概率;/r/n(2)按照/r/n“/r/n平均遇到堵塞次數(shù)最少/r/n”/r/n的要求,請(qǐng)你幫助小李從上述兩條路線中選擇一條最好的旅游路線,并說(shuō)明理由/r/n./r/n22/r/n./r/n(12/r/n分/r/n)某車(chē)間在兩天內(nèi),每天生產(chǎn)10件產(chǎn)品,其中第一天、第二天分別生產(chǎn)了1件、2件次品/r/n./r/n質(zhì)檢部每天要在生產(chǎn)的10件產(chǎn)品中隨意抽取4件進(jìn)行檢查,若發(fā)現(xiàn)有次品,則當(dāng)天的產(chǎn)品不能通過(guò)/r/n./r/n(1)求兩天全部通過(guò)檢查的概率;/r/n(2)若廠內(nèi)對(duì)該車(chē)間生產(chǎn)的產(chǎn)品質(zhì)量采用獎(jiǎng)懲制度,兩天全不通過(guò)檢查罰300元,通過(guò)1天、2天分別獎(jiǎng)300元、900元/r/n./r/n那么該車(chē)間在這兩天內(nèi)得到獎(jiǎng)金的均值是多少元?/r/n

/r/n第七章測(cè)評(píng)/r/n1/r/n./r/nC/r/n/r/n公式/r/nE/r/n(/r/nX/r/n)/r/n=np/r/n并不適用于所有的離散型隨機(jī)變量的均值的計(jì)算/r/n,/r/n只適用于某些離散型隨機(jī)變量/r/n,/r/n故選/r/nC/r/n./r/n2/r/n./r/nA/r/n/r/n由/r/n1/r/n5/r/n+a=/r/n1,/r/n得/r/na=/r/n4/r/n5/r/n,/r/n所以/r/nE/r/n(/r/nX/r/n)/r/n=/r/n0/r/n×/r/n1/r/n3/r/n./r/nB/r/nP/r/n(/r/nX/r/n≤/r/n2)/r/n=/r/n[1/r/n-P/r/n(2/r/n≤/r/nX/r/n≤/r/n6)]/r/n×/r/n1/r/n2/r/n=/r/n[1/r/n-P/r/n(4/r/n-/r/n2/r/n≤/r/nX/r/n≤/r/n4/r/n+/r/n2)]/r/n×/r/n1/r/n2/r/n=/r/n(1/r/n-/r/n0/r/n./r/n9545)/r/n×/r/n1/r/n4/r/n./r/nA/r/n/r/n對(duì)于/r/nA,/r/n總體分為明確的兩類(lèi)/r/n,/r/n但/r/nA/r/n中的隨機(jī)變量/r/nX/r/n不是抽取樣本中一類(lèi)元素的個(gè)數(shù)/r/n,/r/n∴/r/nA/r/n不服從超幾何分布/r/n,/r/n其余各項(xiàng)服從超幾何分布/r/n./r/n故選/r/nA/r/n./r/n5/r/n./r/nD/r/n/r/n記/r/n“/r/n第一次摸到正品/r/n”/r/n為事件/r/nA/r/n,/r/n“/r/n第二次摸到正品/r/n”/r/n為事件/r/nB/r/n,/r/n則/r/nP/r/n(/r/nA/r/n)/r/n=/r/nC/r/n6/r/n1/r/nC/r/n9/r/n1/r/nC/r/n10/r/n故/r/nP/r/n(/r/nB|A/r/n)/r/n=/r/nP/r/n6/r/n./r/nC/r/n/r/n由題意得/r/nP/r/n(/r/nX/r/n≥/r/n1)/r/n=P/r/n(/r/nX=/r/n1)/r/n+P/r/n(/r/nX=/r/n2)/r/n=/r/nC/r/n2/r/n1/r/np/r/n(1/r/n-p/r/n)/r/n+/r/nC/r/n2/r/n2/r/np/r/n2/r/n=/r/n5/r/n9/r/n,/r/n所以/r/np=/r/n1/r/n3/r/np=/r/n5/r/n3/r/n舍去/r/n,/r/n則/r/nY~B/r/n故/r/nD/r/n(/r/nY/r/n)/r/n=/r/n3/r/n×/r/n1/r/n3/r/n×/r/n1/r/n-/r/n1/r/n3/r/n=/r/n所以/r/nD/r/n(3/r/nY+/r/n1)/r/n=/r/n9/r/nD/r/n(/r/nY/r/n)/r/n=/r/n9/r/n×/r/n2/r/n3/r/n=/r/n7/r/n./r/nA/r/n/r/n根據(jù)題意/r/n,/r/n記該同學(xué)未通過(guò)測(cè)試為事件/r/nA/r/n,/r/n該同學(xué)每次投籃投中的概率為/r/n0/r/n./r/n8,/r/n則投不中的概率為/r/n1/r/n-/r/n0/r/n./r/n8/r/n=/r/n0/r/n./r/n2,/r/n事件/r/nA/r/n包含/r/n2/r/n種情況/r/n,/r/n該同學(xué)/r/n5/r/n次都沒(méi)有投中和只投中/r/n1/r/n次/r/n,/r/n則/r/nP/r/n(/r/nA/r/n)/r/n=/r/nC/r/n5/r/n4/r/n(0/r/n./r/n2)/r/n4/r/n×/r/n0/r/n./r/n8/r/n+/r/n(0/r/n./r/n2)/r/n5/r/n=/r/n0/r/n./r/n00672,/r/n故選/r/n8/r/n./r/nA/r/n/r/n根據(jù)題意/r/n,/r/n每個(gè)坑需要補(bǔ)種的概率是相等的/r/n,/r/n都是/r/n1/r/n2/r/n3/r/n=/r/n1/r/n8/r/n,/r/n所以此問(wèn)題相當(dāng)于獨(dú)立重復(fù)試驗(yàn)/r/n,/r/n做了三次/r/n,/r/n每次發(fā)生的概率都是/r/n1/r/n8/r/n,/r/n所以需要補(bǔ)種的坑的均值為/r/n3/r/n×/r/n1/r/n8/r/n=/r/n3/r/n8/r/n9/r/n./r/nAD/r/n/r/n由直方圖可知/r/n,A/r/n校學(xué)生做作業(yè)時(shí)長(zhǎng)大部分在/r/n1/r/n~/r/n2/r/n小時(shí)/r/n,/r/n而/r/nB/r/n校學(xué)生做作業(yè)時(shí)長(zhǎng)大部分在/r/n2/r/n./r/n5/r/n~/r/n3/r/n./r/n5/r/n小時(shí)/r/n,/r/n故/r/nA/r/n正確/r/n,C/r/n錯(cuò)誤/r/n;B/r/n校有學(xué)生做作業(yè)時(shí)長(zhǎng)小于/r/n1/r/n小時(shí)的/r/n,/r/n而/r/nA/r/n校有學(xué)生做作業(yè)時(shí)長(zhǎng)超過(guò)/r/n5/r/n小時(shí)的/r/n,/r/n故/r/nB/r/n錯(cuò)誤/r/n;B/r/n校學(xué)生做作業(yè)時(shí)長(zhǎng)分布相對(duì)/r/nA/r/n校更對(duì)稱(chēng)/r/n,/r/n所以更接近正態(tài)分布/r/n,/r/n故/r/nD/r/n正確/r/n./r/n故選/r/nAD/r/n./r/n10/r/n./r/nACD/r/n/r/n甲罐中有/r/n3/r/n個(gè)紅球、/r/n2/r/n個(gè)黑球/r/n,/r/n乙罐中有/r/n2/r/n個(gè)紅球、/r/n2/r/n個(gè)黑球/r/n,/r/n先從甲罐中隨機(jī)取出一球放入乙罐/r/n,/r/n以/r/nA/r/n表示事件/r/n“/r/n由甲罐取出的球是紅球/r/n”/r/n,/r/n再?gòu)囊夜拗须S機(jī)取出一球/r/n,/r/n以/r/nB/r/n表示事件/r/n“/r/n由乙罐取出的球是紅球/r/n”/r/n,/r/n對(duì)于/r/nA,/r/n易知/r/nP/r/n(/r/nA/r/n)/r/n=/r/n3/r/n5/r/n,/r/n故/r/nA/r/n正確/r/n對(duì)于/r/nB,/r/nP/r/n(/r/nAB/r/n)/r/n=/r/n3/r/n5/r/n∴/r/nP/r/n(/r/nB|A/r/n)/r/n=/r/nP/r/n(/r/nAB/r/n)/r/nP/r/n(/r/n對(duì)于/r/nC,/r/nP/r/n(/r/nA/r/n)/r/n=/r/n2/r/n5/r/n,/r/nP/r/n(/r/nB|/r/nA/r/n)/r/n=/r/nP/r/n∴/r/n由全概率公式得/r/nP/r/n(/r/nB/r/n)/r/n=P/r/n(/r/nA/r/n)/r/nP/r/n(/r/nB|A/r/n)/r/n+P/r/n(/r/nA/r/n)/r/nP/r/n(/r/nB|/r/nA/r/n)/r/n=/r/n3/r/n5/r/n×/r/n3/r/n5/r/n+/r/n對(duì)于/r/nD,/r/n由貝葉斯公式得/r/nP/r/n(/r/nA|B/r/n)/r/n=/r/nP/r/n(/r/nA/r/n)/r/nP/r/n(/r/n故選/r/nACD/r/n./r/n11/r/n./r/nBC/r/n/r/n從裝有大小相同的/r/n3/r/n個(gè)白球和/r/nm/r/n個(gè)黑球的布袋中隨機(jī)摸取一個(gè)球/r/n,/r/n有放回地摸取/r/n5/r/n次/r/n,/r/n每次取到白球的概率為/r/n3/r/n3+/r/nm/r/n,/r/n∵/r/n有放回地摸取/r/n5/r/n次/r/n,/r/n摸得白球個(gè)數(shù)為/r/n∴/r/nX~B/r/n5,/r/n3/r/n3+/r/nm/r/n,/r/n∵/r/nE/r/n(/r/nX/r/n)/r/n=/r/n3,/r/n∴/r/nE/r/n(/r/nX/r/n)/r/n=/r/n5/r/n×/r/n3/r/n3+/r/nm/r/n=/r/n3,/r/n∴/r/nD/r/n(/r/nX/r/n)/r/n=/r/n5/r/n×/r/n12/r/n./r/nBD/r/n/r/n由/r/nn/r/n次獨(dú)立重復(fù)試驗(yàn)的概率計(jì)算公式可知/r/n,/r/nP/r/nk/r/n=/r/nC/r/n6/r/nk/r/n×/r/n2/r/n3/r/nk/r/n×/r/n1/r/n-/r/n2/r/n3/r/n6/r/n-k/r/n∴/r/nP/r/n1/r/n=/r/nC/r/n6/r/n1/r/n×/r/n2/r/n3/r/n1/r/n×/r/n1/r/n3/r/n5/r/n=/r/n4/r/n243/r/n,/r/nP/r/n5/r/n=/r/nC/r/n6/r/n5/r/n×/r/n2/r/n3/r/n5/r/n×/r/n1/r/n3/r/n1/r/n=/r/n64/r/n243/r/n,/r/n顯然/r/nP/r/n1/r/n<P/r/n5/r/n,/r/n故選項(xiàng)/r/nA/r/n錯(cuò)誤/r/n,/r/n由必然事件的概率可知/r/n,/r/n∑/r/nk/r/n=0/r/n6/r/nP/r/nk/r/n=/r/n1,/r/n而/r/nP/r/n0/r/n=/r/nC/r/n6/r/n0/r/n×/r/n2/r/n3/r/n0/r/n×/r/n1/r/n3/r/n6/r/n≠/r/n0,/r/n根據(jù)二項(xiàng)分布概率公式/r/n,/r/n可得/r/nP/r/n0/r/n=/r/n1/r/n729/r/n,/r/nP/r/n1/r/n=/r/n4/r/n243/r/n,/r/nP/r/n2/r/n=/r/n20/r/n243/r/n,/r/nP/r/n3/r/n=/r/n160/r/n729/r/n,/r/nP/r/n4/r/n=/r/n80/r/n243/r/n,/r/nP/r/n5/r/n=/r/n64/r/n243/r/n,/r/nP/r/n6/r/n=/r/n64/r/n729/r/n,/r/n∴/r/nP/r/n0/r/n,/r/nP/r/n1/r/n,/r/nP/r/n2/r/n,/r/n…/r/n,/r/nP/r/n6/r/n中最大的為/r/n13/r/n./r/n5/r/n4/r/n/r/n10/r/n9/r/n/r/n由題意可得/r/n,/r/nC/r/nm/r/n1/r/nC/r/nn/r/n1/r/nC/r/n9/r/n2/r/n=/r/n5/r/n9/r/n,/r/n故/r/nm/r/nn/r/n=/r/n5/r/n4/r/n,/r/n由題意可知/r/n所以/r/nE/r/n(/r/nξ/r/n)/r/n=/r/n2/r/n×/r/n14/r/n./r/n300/r/n/r/n∵/r/n單個(gè)果品的質(zhì)量/r/nξ/r/n(/r/n單位/r/n:g)/r/n近似服從正態(tài)分布/r/nN/r/n(90,/r/nσ/r/n2/r/n),/r/n且/r/nP/r/n(86/r/n</r/nξ/r/n≤/r/n90)/r/n=/r/n0/r/n./r/n2,/r/n∴/r/nP/r/n(90/r/n≤/r/nξ/r/n</r/n94)/r/n=/r/n0/r/n./r/n2,/r/n∴/r/nP/r/n(/r/nξ/r/n≥/r/n94)/r/n=/r/n1/r/n-/r/n2×0/r/n./r/n2/r/n故估計(jì)單個(gè)果品質(zhì)量不低于/r/n94g/r/n的橘果個(gè)數(shù)為/r/n0/r/n./r/n3/r/n×/r/n1000/r/n=/r/n300/r/n./r/n15/r/n./r/n9/r/n22/r/n/r/n由題意/r/nA/r/n1/r/n,/r/nA/r/n2/r/n,/r/nA/r/n3/r/n是兩兩互斥的事件/r/n,/r/n且/r/nA/r/n1/r/n∪/r/nA/r/n2/r/n∪/r/nA/r/n3/r/n所以/r/nP/r/n(/r/nB/r/n)/r/n=P/r/n[/r/nB/r/n∩/r/n(/r/nA/r/n1/r/n∪/r/nA/r/n2/r/n∪/r/nA/r/n3/r/n)]/r/n=P/r/n(/r/nBA/r/n1/r/n)/r/n+P/r/n(/r/nBA/r/n2/r/n)/r/n+P/r/n(/r/nBA/r/n3/r/n)/r/n=P/r/n(/r/nA/r/n1/r/n)/r/nP/r/n(/r/nB|A/r/n1/r/n)/r/n+P/r/n(/r/nA/r/n2/r/n)/r/nP/r/n(/r/nB|A/r/n2/r/n)/r/n+P/r/n(/r/nA/r/n3/r/n)/r/nP/r/n(/r/nB|A/r/n3/r/n)/r/n=/r/n5/r/n16/r/n./r/n2/r/n3/r/n/r/n23/r/n12/r/n/r/n對(duì)給出的/r/n3/r/n個(gè)問(wèn)題/r/n,/r/n∵/r/n教師甲恰好答對(duì)/r/n3/r/n個(gè)問(wèn)題的概率是/r/n1/r/n4/r/n∴/r/n3/r/n4/r/n×/r/n1/r/n2/r/n×/r/n設(shè)隨機(jī)變量/r/nX/r/n表示教師甲答對(duì)題目的個(gè)數(shù)/r/n,/r/n則/r/nX/r/n的可能取值為/r/n0,1,2,3,/r/nP/r/n(/r/nX=/r/n0)/r/n=/r/n1/r/n-/r/n3/r/n4/r/n×/r/n1/r/n-/r/n1/r/n2/r/n×/r/n1/r/n-/r/n2/r/n3/r/n=/r/n1/r/n24/r/n,/r/nP/r/n(/r/nX=/r/n1)/r/n=/r/n3/r/n4/r/n×/r/n1/r/n-/r/n1/r/n2/r/n×/r/n1/r/n-/r/n2/r/n3/r/n+/r/n1/r/n-/r/n3/r/n4/r/n×/r/n1/r/n2/r/n×/r/n1/r/n-/r/n2/r/n3/r/n+/r/n1/r/n-/r/n3/r/n4/r/n×/r/n1/r/n-/r/n1/r/n2/r/n×/r/n2/r/n3/r/nP/r/n(/r/nX=/r/n2)/r/n=/r/n3/r/n4/r/n×/r/n1/r/n2/r/n×/r/n1/r/n-/r/n2/r/n3/r/n+/r/n3/r/n4/r/n×/r/n1/r/n-/r/n1/r/n2/r/n×/r/n2/r/n3/r/n+/r/nP/r/n(/r/nX=/r/n3)/r/n=/r/n1/r/n4/r/n∴/r/nE/r/n(/r/nX/r/n)/r/n=/r/n0/r/n×/r/n1/r/n24/r/n+/r/n1/r/n×/r/n1/r/n4/r/n+/r/n2/r/n17/r/n./r/n解/r/n(1)/r/n設(shè)/r/nA/r/n1/r/n表示事件/r/n“/r/n日銷(xiāo)售量不低于/r/n100/r/n個(gè)/r/n”/r/n,/r/nA/r/n2/r/n表示事件/r/n“/r/n日銷(xiāo)售量低于/r/n50/r/n個(gè)/r/n”/r/n,/r/nB/r/n表示事件/r/n“/r/n在未來(lái)連續(xù)/r/n3/r/n天里/r/n,/r/n有連續(xù)/r/n2/r/n天的日銷(xiāo)售量不低于/r/n100/r/n個(gè)且另一天銷(xiāo)售量低于/r/n50/r/n個(gè)/r/n”/r/n./r/n因此/r/nP/r/n(/r/nA/r/n1/r/n)/r/n=/r/n(0/r/n./r/n006/r/n+/r/n0/r/n./r/n004/r/n+/r/n0/r/n./r/n002)/r/n×/r/n50/r/n=/r/n0/r/n./r/n6,/r/nP/r/n(/r/nA/r/n2/r/n)/r/n=/r/n0/r/n./r/n003/r/n×/r/n50/r/n=/r/n0/r/n./r/n15,/r/nP/r/n(/r/nB/r/n)/r/n=/r/n0/r/n./r/n6/r/n×/r/n0/r/n./r/n6/r/n×/r/n0/r/n./r/n15/r/n×/r/n2/r/n=/r/n0/r/n./r/n108/r/n./r/n(2)/r/nX/r/n可能取的值為/r/n0,1,2,3,/r/n相應(yīng)的概率為/r/nP/r/n(/r/nX=/r/n0)/r/n=/r/nC/r/n3/r/n0/r/n·/r/n(1/r/n-/r/n0/r/n./r/n6)/r/n3/r/n=/r/nP/r/n(/r/nX=/r/n1)/r/n=/r/nC/r/n3/r/n1/r/n·/r/n0/r/n./r/n6/r/n×/r/n(1/r/n-/r/n0/r/n./r/n6)/r/n2/r/n=/r/nP/r/n(/r/nX=/r/n2)/r/n=/r/nC/r/n3/r/n2/r/n·/r/n0/r/n./r/n6/r/n2/r/n×/r/n(1/r/n-/r/n0/r/n./r/n6)/r/n=/r/nP/r/n(/r/nX=/r/n3)/r/n=/r/nC/r/n3/r/n3/r/n·/r/n0/r/n./r/n6/r/n3/r/n=/r/n0/r/n故/r/nX/r/n的分布列為/r/nX/r/n0/r/n1/r/n2/r/n3/r/nP/r/n0/r/n./r/n064/r/n0/r/n./r/n288/r/n0/r/n./r/n432/r/n0/r/n./r/n216/r/n因?yàn)?r/nX~B/r/n(3,0/r/n./r/n6),/r/n所以/r/nE/r/n(/r/nX/r/n)/r/n=/r/n3/r/n×/r/n0/r/n./r/n6/r/n=/r/n1/r/n./r/n8,/r/nD/r/n(/r/nX/r/n)/r/n=/r/n3/r/n×/r/n0/r/n./r/n6/r/n×/r/n(1/r/n-/r/n0/r/n./r/n6)/r/n=/r/n0/r/n./r/n72/r/n./r/n18/r/n./r/n解/r/n因?yàn)?r/nξ/r/n~N/r/n(90,100),/r/n所以/r/nμ/r/n=/r/n90,/r/nσ/r/n=/r/n100/r/n=/r/n10/r/n./r/n(1)/r/n由于正態(tài)變量在區(qū)間/r/n[/r/nμ/r/n-/r/n2/r/nσ/r/n,/r/nμ/r/n+/r/n2/r/nσ/r/n]/r/n內(nèi)取值的概率是/r/n0/r/n./r/n9545,/r/n而該正態(tài)分布中/r/n,/r/nμ/r/n-/r/n2/r/nσ/r/n=/r/n90/r/n-/r/n2/r/n×/r/n10/r/n=/r/n70,/r/nμ/r/n+/r/n2/r/nσ/r/n=/r/n90/r/n+/r/n2/r/n×/r/n10/r/n=/r/n110,/r/n于是考試成績(jī)/r/nξ/r/n位于區(qū)間/r/n[70,110]/r/n內(nèi)的概率為/r/n0/r/n./r/n9545/r/n./r/n(2)/r/n由/r/nμ/r/n=/r/n90,/r/nσ/r/n=/r/n10,/r/n得/r/nμ/r/n-/r/nσ/r/n=/r/n80,/r/nμ/r/n+/r/nσ/r/n=/r/n100/r/n./r/n由于正態(tài)變量在區(qū)間/r/n[/r/nμ/r/n-/r/nσ/r/n,/r/nμ/r/n+/r/nσ/r/n]/r/n內(nèi)取值的概率是/r/n0/r/n./r/n6827,/r/n所以考試成績(jī)/r/nξ/r/n位于區(qū)間/r/n[80,100]/r/n內(nèi)的概率是/r/n0/r/n./r/n6827/r/n./r/n一共有/r/n2000/r/n名學(xué)生/r/n,/r/n所以考試成績(jī)?cè)?r/n[80,100]/r/n的考生大約有/r/n2000/r/n×/r/n0/r/n./r/n6827/r/n≈/r/n1365(/r/n人/r/n)/r/n./r/n19/r/n./r/n解/r/n(1)/r/nX/r/n的所有可能取值為/r/n0,1,2,/r/n依題意得/r/nP/r/n(/r/nX=/r/n0)/r/n=/r/nC/r/n4/r/nP/r/n(/r/nX=/r/n1)/r/n=/r/nC/r/n4/r/nP/r/n(/r/nX=/r/n2)/r/n=/r/nC/r/n∴/r/nX/r/n的分布列為/r/nX/r/n0/r/n1/r/n2/r/nP/r/n1/r/n3/r/n1/r/n(2)/r/n設(shè)/r/n“/r/n甲、乙都不被選中/r/n”/r/n為事件/r/nC/r/n,/r/n則/r/nP/r/n(/r/nC/r/n)/r/n=/r/nC/r/n∴/r/n所求概率為/r/nP/r/n(/r/nC/r/n)/r/n=/r/n1/r/n-P/r/n(/r/nC/r/n)/r/n=/r/n1/r/n-/r/n1/r/n(3)/r/nP/r/n(/r/nB/r/n)/r/n=/r/nC/r/n5/r/n2/r/nC/r/n6/r/n3/r/n=/r/n10/r/n20/r/n./r/n解/r/n(1)/r/n由古典概型的概率計(jì)算公式知所求概率為/r/nP=/r/nC/r/n(2)/r/nX/r/n的所有可能值為/r/n1,2,3,/r/n且/r/nP/r/n(/r/nX=/r/n1)/r/n=/r/nC/r/n4/r/nP/r/n(/r/nX=/r/n2)/r/n=/r/nC/r/n3/r/nP/r/n(/r/nX=/r/n3)/r/n=/r/nC/r/n故/r/nX/r/n的分布列為/r/nX/r/n1/r/n2/r/n3/r/nP/r/n17/r/n43/r/n1/r/n從而/r/nE/r/n(/r/nX/r/n)/r/n=/r/n1/r/n×/r/n17/r/n42/r/n+/r/n2/r/n×/r/n43/r/n21/r/n./r/n解/r/n(1)/r/n設(shè)走/r/nL/r/n1/r/n路線最多遇到/r/n1/r/n次堵塞為/r/nA/r/n事件/r/n,/r/n則/r/nP/r/n(/r/nA/r/n)/r/n=/r/nC/r/n3/r/n0/r/n×/r/n1