YOUTUBE_midterm

คณะวทิ ยาศาสตร์และเทคโนโลยี มหาวทิ ยาลยั เทคโนโลยรี าชมงคลธญั บุรีชื่อ–สกุล _______________________________________รหสั นกั ศึกษา ___________________________สาขาวชิ า ___________________ Sec. ____อาจารย์ผู้สอน__________________เลขทตี่ ามใบเซ็นช่ือ ____ สูตรที่ให้สาหรับสอบกลางภาควชิ าหลกั สถิติ 09121015 Nn xi xi1. ค่าเฉลย่ี   i1 , X  i1 Nn2. ส่วนเบยี่ งเบนมาตรฐาน N N n n n n i1 (xi  )2  xi2 (xi  x)2 i1 xi2  x2 ,S  (xi  x)2 xi2 2 n  i1  i1  2 ,S  i1  i1  n 1  nx N N n n 13. ความแปรปรวน NN nn nn     2 (xi  )2  xi2  2 ,S2  (xi  x)2  xi2  x2,S2  (xi  x)2  xi2  nx2 i1 i1 i1 i1 i1 i1 NN nn n 1 n 14. สัมประสิทธ์คิ วามแปรผนัC.V.   100%, C.V.  S.D. 100%, C.V.  S 100% XX5. ความน่าจะเป็ น n Pr  n! , nCr  n! r)! , P(E)  n(E)  n (n  r)! r!(n  n(S) N P(A  B)  P(A)  P(B)  P(A  B)6. การแจกแจงแบบทวนิ าม f  X ;n, p   n  px  q nx   nCx px q nx ; x  0,1, 2,..., n7. การแจกแจงแบบปัวซอง  x    f  X ;   ex ; x  0,1, 2,... x!

จงแสดงวธิ ีทาทุกข้อ หากตอบแต่คาตอบเพยี งอย่างเดยี วจะไม่ได้คะแนนในข้อน้นั ๆ1. กำหนดขอ้ มูลชุดหน่ึงดงั น้ี 30, 1500, 65, 90, 125, 50, 1201.1 จงหำค่ำเฉลี่ย (1 คะแนน)..........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................1.2 จงหำค่ำมธั ยฐำน (1 คะแนน)..........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................1.3 จงหำค่ำฐำนนิยม (1 คะแนน)........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................1.4 จำกขอ้ มลู ชุดน้ี ควรเลือกใชค้ ่ำสถิติใดเป็นตวั แทนขอ้ มูล ถึงจะเหมำะสมที่สุด ดีที่สุด ดว้ ยเหตุผลใด (1 คะแนน)......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................2. ข้อมลู ชดุ หนง่ึ ประกอบด้วยตวั เลข 6 จำนวนคอื 1, 3, 5, 6, 7 และ 82.1จงหำค่ำควำมแปรปรวน (3 คะแนน)................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

2.2 จงหำค่ำส่วนเบ่ียงเบนมำตรฐำน (1 คะแนน)................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................3. จำกขอ้ มลู น้ำหนกั เดก็ ทำรกของโรงพยำบำลแห่งหน่ึงเป็นดงั น้ี โรงพยำบำล A มคี ่ำเฉลยี่ ของน้ำหนกัจำกเดก็ 100 คน เท่ำกบั 2,500 กรัม และส่วนเบ่ียงเบนมำตรฐำนเท่ำกบั 350 กรัม โรงพยำบำล B มีค่ำเฉลีย่ ของน้ำหนกั จำกเดก็ 100 คน เท่ำกบั 8 ปอนด์ และส่วนเบี่ยงเบนมำตรฐำนเท่ำกบั 0.4 ปอนด์จงวเิ ครำะหว์ ่ำน้ำหนกั ของเดก็ ทำรกโรงพยำบำลไหนท่ีมคี วำมแตกต่ำงของน้ำหนกั มำกกว่ำกนั พร้อมให้เหตผุ ลประกอบ (3 คะแนน)................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................4. จงเขียนปริภูมติ วั อยำ่ ง (sample space: S) ของกำรทดลองโยนบำท 1 เหรียญ และลกู เต๋ำ 1 ลูกพร้อมกนัจำนวน 1 คร้ัง (1 คะแนน)..........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................5. นำยบอสตอ้ งกำรแต่งตวั ไปงำนเล้ยี งฉลองข้ึนบำ้ นใหม่ โดยสมชำยมีเส้ือเชิ้ต 7 ตวั กำงเกงขำยำว 4 ตวัถงุ เทำ้ 12 คู่ และรองเทำ้ 2 คู่ จงหำวำ่ นำยบอสสำมำรถแต่งกำยไดก้ ่ีแบบ (1 คะแนน)................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

6. คิมเบอรี่ตอ้ งกำรซ้ือยำสระผมไปใชง้ ำน 1 ขวด จึงเขำ้ ไปในร้ำนสะดวกซ้ือแห่งหน่ึงซ่ึงมยี ำสระผมยห่ี อ้A จำนวน 9 ขวด ยำสระผมยห่ี อ้ B จำนวน 8 ขวด และยำสระผมยห่ี อ้ C จำนวน 12 ขวด จงหำวำ่คิมเบอรี่สำมำรถเลือกไดก้ ี่แบบ (1 คะแนน).....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................7. ครูดำวตอ้ งกำรจดั เด็กนกั เรียน 8 คน ซ่ึงมีเด็กชำยวนั จนั ทร์และเดก็ หญิงเดือนเพญ็ รวมอยดู่ ว้ ย เพือ่ เดินแถวไปข้ึนรถโรงเรียน จงหำจำนวนวธิ ีที่เด็กนกั เรียนท้งั 8 คนจะสำมำรถยนื เขำ้ แถวโดย7.1 ไม่มเี ง่ือนไข (1 คะแนน)...........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................7.2 ตอ้ งกำรใหเ้ ด็กชำยวนั จนั ทร์และเดก็ หญิงเดือนเพญ็ ไม่ยนื ตดิ กนั (1 คะแนน).....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

8. บริษทั แห่งหน่ึงมีพนกั งำนท้งั หมด 20 คน เป็นพนกั งำนผชู้ ำย 12 คน ที่เหลอื เป็นพนกั งำนผหู้ ญิง ผบู้ ริหำรของบริษทั ตอ้ งกำรเลือกตวั แทนจำนวน 3 คน จะสำมำรถจดั ไดก้ ่ีวธิ ี8.1 ถำ้ พนกั งำนทกุ คนสำมำรถเป็นตวั แทนได้ (ไมม่ ีเง่ือนไขใดๆ) (1 คะแนน)........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................8.2 ถำ้ ตอ้ งกำรใหไ้ ดต้ วั แทนเป็นผชู้ ำย 1 คนและผหู้ ญิง 2 คน (1 คะแนน)...........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................9. โยนลกู เต๋ำ 2 ลูกพร้อมกนั 1 คร้ังถำ้ กำหนดให้ A แทน เหตุกำรณ์ที่ผลรวมของแตม้ บนลูกเต๋ำท้งั สองเป็น 7และ B แทน เหตุกำรณ์ท่ีแตม้ ของลกู เต๋ำลกู ที่ 2 ข้ึนแตม้ 4 จงหำ9.1 P(A) (1 คะแนน).................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................9.2 P(B) (1 คะแนน)....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

9.3 P(A  B) (1 คะแนน)...........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................10. กำหนด f(x) = x2 +1 ; x = 1, 2, 3, 4, 5 6010.1 จงหำ P(2 < x < 5) (2 คะแนน).........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................10.2 จงหำ E(3x-2) (4 คะแนน)...........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

11. ให้ X เป็นตวั แปรสุ่มท่ีฟังกช์ นั ควำมหนำแน่น ดงั น้ี x2 ; 0<x<2 ; otherwisef(x) =  4 011.1 จงหำ P(1  x 1.5) (3 คะแนน).....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................11.2 จงหำ V(x) (5 คะแนน)................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

12. เป็นที่ทรำบกนั วำ่ ผหู้ ญิงไทยร้อยละ 80 ทางานนอกบ้าน จำกกำรสอบถำมผหู้ ญิงไทยมำจำนวน 20 คนจงหำควำมน่ำจะเป็นที่จะมผี หู้ ญิงไทยทางานนอกบ้านจำนวน 15 คน (4 คะแนน).........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................13. ร้ำนถ่ำยเอกสำรมลี กู คำ้ โดยเฉลยี่ จำนวน 4 คนต่อชั่วโมง จงหำควำมน่ำจะเป็นท่ีมีลูกคำ้ 2 คนขึน้ ไป ในเวลำครึ่งชั่วโมง (4 คะแนน).........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

14. ให้ X มกี ำรแจกแจงแบบปกติมคี ่ำเฉล่ียเท่ำกบั 50 และส่วนเบี่ยงเบนมำตรฐำนเท่ำกบั 10 จงหำควำมน่ำจะเป็นท่ี X จะมีค่ำอยรู่ ะหว่ำง 48 ถงึ 65 (4 คะแนน)..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................15. จงหำค่ำ a ท่ีทำให้15.1 P(Z > a) = 0.8907 ; ดงั น้นั a =______________________ (1 คะแนน)15.2 P(1< Z < a) = 0.1525 ; ดงั น้นั a =_______________________ (1 คะแนน)16. จำกตำรำงแจกแจงควำมน่ำจะเป็นแบบที จงหำ16.1 t 0.25,28  ____________________________ (1 คะแนน)16.2 t 0.90,8  _____________________________ (1 คะแนน)17. ให้  2 เป็นตวั แปรสุ่มท่ีมกี ำรแจกแจงแบบไคสแควร์ดว้ ยองศำอิสระ จงหำควำมน่ำจะเป็นต่อไปน้ี17.1 P(3.05  2  17.3)  _____________;  11 (1 คะแนน) 17.2 2  22.7)  _____________;  28 (1 คะแนน) จงหำควำมน่ำจะเป็ น P( (1 คะแนน)18. ให้ เป็นตวั แปรสุ่มท่ีมกี ำรแจกแจงแบบ ดว้ ยองศำอสิ ระ และ (1 คะแนน)ต่อไปน้ี18.1 P(1.64  F  2.15) = __________ ;18.2 P(F  2.33) = _______________ ;

19. ถำ้ จำนวนเงินใชจ้ ่ำยตอ่ วนั ของนกั ศกึ ษำคณะเทคโนโลยกี ำรเกษตรมีกำรแจกแจงแบบปกติ ทมี่ คี ่ำเฉลี่ย 200 บำทตอ่ วนั คำ่ ส่วนเบ่ียงเบนมำตรฐำน 20 บำทตอ่ วนั ถำ้ สุ่มตวั อย่างนกั ศึกษำมำ 25 คน จงหำควำมน่ำจะเป็นที่จานวนเงนิ เฉล่ียของนักศึกษา 25 คนน้ีจะน้อยกว่า 210 บำทต่อวนั (5 คะแนน).......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................20. อำยกุ ำรใชง้ ำนของหลอดไฟฟ้ำชนิดหน่ึงมีกำรแจกแจงปกติ มคี ่ำส่วนเบีย่ งเบนมำตรฐำน 1.63 ปี สุ่มตวั อยำ่ งหลอดไฟฟ้ำชนิดน้ีมำ 15 หลอด จงหำควำมน่ำจะเป็นทีค่ ่าส่วนเบ่ียงเบนมาตรฐานของตวั อยำ่ งมีคำ่ มากกว่า 2 ปี(5 คะแนน).......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................21. ถ้ำ s12 และ s22 เป็นควำมแปรปรวนตวั อยำ่ งซึง่ สมุ่ มำจำกประชำกร 2 กลมุ่ ขนาด 26 และ 30ที่เป็นอิสระกนั และมกี ำรแจกแจงแบบปกติท่มี คี วำมแปรปรวนเป็น 10 และ 15 ตำมลำดบั จงหำควำมนำ่ จะเป็นท่ีอตั รำสว่ นควำมแปรปรวนของตวั อยำ่ งของกลมุ่ ที่ 1 และกลมุ่ ท่ี 2 จะมำกกวำ่ 1.26...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................