Question

7£®Îª¿¼²éijÖÖÒßÃçÔ¤·À¼²²¡µÄЧ¹û£¬½øÐж¯ÎïʵÑ飬µÃµ½Í³¼ÆÊý¾ÝÈç±í£º

	δ·¢²¡	·¢²¡	ºÏ¼Æ
δעÉäÒßÃç	20	x	A
×¢ÉäÒßÃç	30	y	B
ºÏ¼Æ	50	50	100

ÏÖ´ÓËùÓÐÊÔÑ鶯ÎïÖÐÈÎÈ¡Ò»Ö»£¬È¡µ½¡°×¢ÉäÒßÃ硱¶¯ÎïµÄ¸ÅÂÊΪ$\frac{2}{5}$£®
£¨1£©Çó2¡Á2ÁÐÁª±íÖеÄÊý¾Ýx£¬y£¬A£¬BµÄÖµ£»
£¨2£©»æÖÆ·¢²¡ÂʵÄÌõÐÎͳ¼Æͼ£¬²¢ÅР¶ÏÒßÃçÊÇ·ñÓÐЧ£¿
£¨3£©Äܹ»Óжà´ó°ÑÎÕÈÏΪÒßÃçÓÐЧ£¿
¸½£ºK²=$\frac{{n{{£¨{ad-bc}£©}^2}}}{{£¨{a+b}£©£¨{c+d}£©£¨{a+c}£©£¨{b+d}£©}}$

P£¨ K2¡ÜK0£©	0.05	0.01	0.005	0.001
K0	3.841	6.635	7.879	10.828

Answer 1

·ÖÎö £¨1£©ÓÉ¡°×¢ÉäÒßÃ硱¶¯ÎïµÄ¸ÅÂÊΪ$\frac{2}{5}$£¬¿ÉµÃ$\frac{y+30}{100}=\frac{2}{5}$£¬ÇóµÃyÖµ£¬½øÒ»²½ÇóµÃxÓëAµÄÖµ£»
£¨2£©ÓÉͼ±íÖ±½ÓÇó³öδעÉäÒßÃç·¢²¡ÂÊΪ$\frac{40}{60}=\frac{2}{3}$£¬×¢ÉäÒßÃç·¢²¡ÂÊΪ$\frac{10}{40}=\frac{1}{4}$£®²¢×÷³ö·¢²¡ÂʵÄÌõÐÎͳ¼Æͼ£¬ÓÉͼµÃµ½ÒßÃçÓÐЧ£»
£¨3£©ÓÉ2¡Á2ÁÐÁª±íÇó³öK²µÄÖµ£¬¶ÔÓ¦¸½±íµÃ´ð°¸£®

½â´ð ½â£º£¨1£©Éè¡°´ÓËùÓÐÊÔÑ鶯ÎïÖÐÈÎÈ¡Ò»Ö»£¬È¡µ½¡°×¢ÉäÒßÃ硱¶¯ÎΪʼþ M£¬
ÓÉÒÑÖªµÃP£¨M£©=$\frac{y+30}{100}=\frac{2}{5}$£¬
¡ày=10£¬B=40£¬x=40£¬A=60£®¡­£¨5·Ö£©
£¨2£©Î´×¢ÉäÒßÃç·¢²¡ÂÊΪ$\frac{40}{60}=\frac{2}{3}$£¬×¢ÉäÒßÃç·¢²¡ÂÊΪ$\frac{10}{40}=\frac{1}{4}$£®
·¢²¡ÂʵÄÌõÐÎͳ¼ÆͼÈçͼËùʾ£¬¡­£¨7·Ö£©
ÓÉͼ¿ÉÒÔ¿´³öÒßÃçÓÐЧ£®¡­£¨8·Ö£©

£¨3£©${{K}^2}=\frac{{100{{£¨{20¡Á10-30¡Á40}£©}^2}}}{50¡Á50¡Á40¡Á60}$¡­£¨9·Ö£©
=$\frac{1000000}{50¡Á20¡Á60}=\frac{50}{3}¡Ö16.67£¾10.828$£®¡­£¨11·Ö£©
¹ÊÓÐ99.9%µÄ°ÑÎÕÈÏΪÒßÃçÓÐЧ£®¡­£¨12·Ö£©

µãÆÀ ±¾Ì⿼²é¶ÀÁ¢ÐÔ¼ìÑéµÄÓ¦Ó㬿¼²éÁËѧÉú¶Áȡͼ±íµÄÄÜÁ¦£¬¿¼²é¼ÆËãÄÜÁ¦£¬ÊÇÖеµÌ⣮