Question

9£®Ä³¸ßУ¾­¼Ã¹ÜÀíѧԺÔÚ2014Äê11ÔÂ11ÈÕ¡°Ë«11¹ºÎï½Ú¡±Æڼ䣬¶Ô[25£¬55]ËêµÄÈËȺËæ»ú³éÈ¡ÁË100È˽øÐе÷²é£¬µÃµ½¸÷ÄêÁä¶ÎÈËÊýƵÂÊ·Ö²¼Ö±·½Í¼£®Í¬Ê±¶ÔÕâ100ÈËÊÇ·ñ²Î¼Ó¡°ÉÌÆ·ÇÀ¹º¡±½øÐÐͳ¼Æ£¬½á¹ûÈçÏÂ±í£º
£¨1£©Çóͳ¼Æ±íÖÐaºÍpµÄÖµ£»
£¨2£©´ÓÄêÁäÂäÔÚ£¨40£¬50]ÄڵIJμӡ°ÉÌÆ·ÇÀ¹º¡±µÄÈËȺÖУ¬²ÉÓ÷ֲã³éÑù·¨³éÈ¡6È˲μÓÂúÒâ¶Èµ÷²é£¬ÔÚ³éÈ¡µÄ6ÈËÖУ¬ÓÐËæ»úµÄ2È˸е½¡°ÂúÒ⡱£¬Éè¸Ðµ½¡°ÂúÒ⡱µÄ2ÈËÖÐÄêÁäÔÚ£¨40£¬45]ÄÚµÄÈËÊýΪX£¬ÇóXµÄ·Ö²¼ÁкÍÊýѧÆÚÍû£®
£¨3£©Í¨¹ýÓÐûÓÐ95%µÄ°ÑÎÕÈÏΪ£¬½øÐС°ÉÌÆ·ÇÀ¹º¡±Óë¡°ÄêÁäµÍÓÚ40ËꡱÓйأ¿ËµÃ÷ÄãµÄÀíÓÉ£®

×éÊý	·Ö×é	ÇÀ¹ºÉÌÆ·µÄÈËÊý	Õ¼±¾×éµÄƵÂÊ
µÚÒ»×é	[25£¬30£©	12	0.6
µÚ¶þ×é	[30£¬35£©	18	p
µÚÈý×é	[35£¬40£©	10	0.5
µÚËÄ×é	[40£¬45£©	a	0.4
µÚÎå×é	[45£¬50£©	3	0.3
µÚÁù×é	[50£¬55£©	1	0.2

¸½£ºK²=$\frac{n£¨ad-bc£©2}{£¨a+b£©£¨c+d£©£¨a+c£©£¨b+d£©}$

P£¨¦Ö2¡Ýk£©	0.100	0.050	0.010	0.001
k	2.706	3.841	6.635	10.828

Answer 1

·ÖÎö £¨1£©¸ù¾ÝƵÂÊ¡¢ÆµÊýÓëÑù±¾ÈÝÁ¿µÄ¹Øϵ£¬ÀûÓÃƵÂÊ·Ö²¼Ö±·½Í¼ºÍƵÂÊ·Ö²¼±í£¬Çó³öa¡¢pµÄÖµ£»
£¨2£©ÒÀÌâÒ⣬Çó³öXµÄ¿ÉÄÜÈ¡Öµ£¬¼ÆËã¶ÔÓ¦µÄ¸ÅÂÊ£¬¼´µÃXµÄ·Ö²¼ÁУ¬¼ÆËãÊýѧÆÚÍûÖµE£¨X£©£»
£¨3£©»­³ö2¡Á2ÁÐÁª±í£¬¼ÆËã¹Û²âÖµK²£¬¶ÔÕÕÊýÖµ±í¼´¿ÉµÃ³öͳ¼Æ½áÂÛ£®

½â´ð ½â£º£¨1£©ÒòΪ×ÜÈËÊýΪ100£¬
ËùÒÔÔÚ[40£¬45£©ËêµÄÈËÊýΪ100¡Á5¡Á0.03=15£¬
ËùÒÔa=15¡Á0.4=6£»
ÒòΪÄêÁäÔÚ[30£¬35£©ËêµÄÈËÊýµÄƵÂÊΪ
1-5¡Á£¨0.04+0.04+0.03+0.02+0.01£©=0.3£¬
ËùÒÔÄêÁäÔÚ[30£¬35£©ËêµÄÈËÊýΪ100¡Á0.3=30£¬
ËùÒÔp=$\frac{18}{30}$=0.6£»
£¨2£©ÒÀÌâÒ⣬³éÈ¡ÄêÁäÔÚ[40£¬45£©ËêÖ®¼ä4ÈË£¬³éÈ¡ÄêÁäÔÚ[45£¬50£©ËêÖ®¼ä2ÈË£¬
X¿ÉÒÔÈ¡0£¬1£¬2£»
P£¨X=0£©=$\frac{{C}_{2}^{2}}{{C}_{6}^{2}}$=$\frac{1}{15}$£¬P£¨X=1£©=$\frac{{C}_{4}^{1}{•C}_{2}^{1}}{{C}_{6}^{2}}$=$\frac{8}{15}$£¬P£¨X=2£©=$\frac{{C}_{4}^{2}}{{C}_{6}^{2}}$=$\frac{6}{15}$£»
ËùÒÔXµÄ·Ö²¼ÁÐΪ

X	0	1	2
P	$\frac{1}{15}$	$\frac{8}{15}$	$\frac{6}{15}$

ËùÒÔE£¨X£©=0¡Á$\frac{1}{15}$+1¡Á$\frac{8}{15}$+2¡Á$\frac{6}{15}$=$\frac{4}{3}$£»
£¨3£©¿ÉµÃ2¡Á2ÁÐÁª±íΪ

	ÄêÁäÔÚ40ÒÔÏÂ	ÄêÁä²»ÔÚ40ÒÔÏÂ	ºÏ¼Æ
²Î¼ÓÇÀ¹º	40	10	50
δ²Î¼ÓÇÀ¹º	30	20	50
ºÏ¼Æ	70	30	100

¼ÆËãK²=$\frac{100}{21}=4.762£¾3.841$£¬
Òò´ËÓÐ95%µÄ°ÑÎÕÈÏΪ£¬½øÐС°ÉÌÆ·ÇÀ¹º¡±Óë¡°ÄêÁäµÍÓÚ40ËꡱÓйأ®

µãÆÀ ±¾Ì⿼²éÁËÀëÉ¢ÐÍËæ»ú±äÁ¿µÄ·Ö²¼ÁÐÓëÊýѧÆÚÍûµÄ¼ÆËãÎÊÌ⣬Ҳ¿¼²éÁ˶ÀÁ¢ÐÔ¼ìÑéµÄÓ¦ÓÃÎÊÌ⣬ÊÇ×ÛºÏÐÔÌâÄ¿£®