为监控某条生产线上产品的质量,检测员每隔相同时间抽取一件产品,并测量其尺寸,在一天的抽检结束后,检测员将测得的各数据按从小到大的顺序整理成如下表格:
编号 |
① |
② |
③ |
④ |
⑤ |
⑥ |
⑦ |
⑧ |
⑨ |
⑩ |
⑪ |
⑫ |
⑬ |
⑭ |
⑮ |
尺寸![](/wiris/showimage?formula=E2240C103FF8E0DFE797FCDBD6A15AF5BEF16354BE18785C17DE68AD2A7C44C998380531A7F73EC55F5CB5D0D84294B47D8F75B9E7829A00862D53B239B3BAE979DEF822831533D96590AB51EEA64A3224D94C5F70D64F35E13C1D177937EAD0FE2262F9B7DE429CC3CD62E13E4C8179) |
8.72 |
8.88 |
8.92 |
8.93 |
8.94 |
8.96 |
8.97 |
8.98 |
![](/wiris/showimage?formula=B63926967B6C93A893ACADC1B0E475AD780E437680C2F6F90FE2BFFD56BAAA0198380531A7F73EC55F5CB5D0D84294B47D8F75B9E7829A00862D53B239B3BAE979DEF822831533D96590AB51EEA64A3224D94C5F70D64F35E13C1D177937EAD0FE2262F9B7DE429CC3CD62E13E4C8179)
|
9.03 |
9.04 |
9.06 |
9.07 |
9.08 |
![](/wiris/showimage?formula=A8F5278530D5C50FF9647897237FE3B8B111FF3B7D5468092821CD30CC8A593798380531A7F73EC55F5CB5D0D84294B47D8F75B9E7829A00862D53B239B3BAE979DEF822831533D96590AB51EEA64A3224D94C5F70D64F35E13C1D177937EAD0FE2262F9B7DE429CC3CD62E13E4C8179)
|
按照生产标准,产品等次规定如下:
尺寸(单位:![](/wiris/showimage?formula=817A1084EF213AAFD1F756B074BAA1BE8650979F42C2130EB0B9CA281C8F7EA198380531A7F73EC55F5CB5D0D84294B47D8F75B9E7829A00862D53B239B3BAE979DEF822831533D96590AB51EEA64A3224D94C5F70D64F35E13C1D177937EAD0FE2262F9B7DE429CC3CD62E13E4C8179) |
产品等次 |
![](/wiris/showimage?formula=F97BD8E8EC3A15C19C80CD2A156D97E9613DE82D12E52AD027F9687F2592BD7898380531A7F73EC55F5CB5D0D84294B47D8F75B9E7829A00862D53B239B3BAE979DEF822831533D96590AB51EEA64A3224D94C5F70D64F35E13C1D177937EAD0FE2262F9B7DE429CC3CD62E13E4C8179)
|
特等品 |
![](/wiris/showimage?formula=6FA16028187907A6544A8B690CAAC8982DE8D57B9867426A2A9DB77DCC8EFCCC98380531A7F73EC55F5CB5D0D84294B47D8F75B9E7829A00862D53B239B3BAE979DEF822831533D96590AB51EEA64A3224D94C5F70D64F35E13C1D177937EAD0FE2262F9B7DE429CC3CD62E13E4C8179)
|
优等品 |
![](/wiris/showimage?formula=77BE5F0D4A721184D18C2D627EE9C97B85059D8553AFD70B7F509E5DBBC1679398380531A7F73EC55F5CB5D0D84294B47D8F75B9E7829A00862D53B239B3BAE979DEF822831533D96590AB51EEA64A3224D94C5F70D64F35E13C1D177937EAD0FE2262F9B7DE429CC3CD62E13E4C8179)
|
合格品 |
或![](/wiris/showimage?formula=A36B48BEA7380559E1B81186DB6C31382502B303208AF6BBEE252716040169E098380531A7F73EC55F5CB5D0D84294B47D8F75B9E7829A00862D53B239B3BAE979DEF822831533D96590AB51EEA64A3224D94C5F70D64F35E13C1D177937EAD0FE2262F9B7DE429CC3CD62E13E4C8179)
|
非合格品 |
注:在统计优等品个数时,将特等品计算在内;在统计合格品个数时,将优等品(含特等品)计算在内.
(1)已知此次抽检的合格率为
,请判断编号为⑮的产品是否为合格品,并说明理由.
(2)已知此次抽检出的优等品尺寸的中位数为
.
求
的值;
将这些优等品分成两组,一组尺寸大于
,另一组尺寸不大于
,从这两组中各随机抽取1件进行复检,求抽到的2件产品都是特等品的概率.