. -
()
-... -............. (3)
... (Descrptve Statstcs) (Inferental Statstc). (Statstc). --.... " " ".." " " " "...... (4)
-.... 0.. (0, 0). 3.5...0.60 o.3 0.7 :...... 4 5 3. 6.... Varable (5)
...... --.............. (6)
-..(Parameters).. ( ). (Statstcs). -..... ()...... (7)
.....( ) ( ). -- 80 --.. 80 :--.(--) 5 "".5 " ". (8)
:-- 5 8 3 9 80 -.. -- 0 3--.. :3-- 3 6 6 7 5 3 3 7 6 3 7 4 7 6 4 4 5 3 7 6 7 3 7 4 6 3 6 3 5 4 4 3 3 7 5 5 5 7 3 5 7 3 5 6 4 5 3 6 7 6 3 3 5 6 3 5 3 7 6 3 7 5 6 4 3 5 4 3 7 6 3 7 6 3 6 4 5 5 3 6 3 6 3 5 7 5 7 7.4-- (9)
. 7 4 0 4.0 :4-- 3 4 5 6 7 8 5 5 0 7 8 7 0.. 3--. 44 5--. 44 :5-- 0 8 6 7 9 6 4 3 6 8 0 9 9 6 3 5 3 7 7 8 9 7 0 6 7 8 3 0 6 0 9 6 7 6 6 8 0 0 6 4 9 0 8 9 7 4 4 4 0 4 7 4 5 0 4 8 7 5 8 8 0 4 0 7 6 6 7 5 9 6 5 3 6 4 3 5 0 3 0 5 8 4 9 9 3 9 0 7 6 4 9 6 8 7 3 9 5 7 4 7 6 5 0 9 8 6 9 3 5 3 5 4 0 9 3 9 0 0 6 5 (0)
- 0..6-- :6--,,3,4 5,6,7,8 9,0,, 3,4,5,6 7,8,9,0 3 33 9 8 44.. : b a a - b "a - b" "b a ".b a... : ()
R Max Mn : R () Max Mn.. " < b".b : " a". : K R + L () R + L K (3) K R L. ()
. ( 3) - ( L ) ( K ).. ( + ) a - a L. ( ) a a + L a a + L L K : a - a +,,..., K (4) ( F ). ( F %) F ( ) F 7--. n. 00 F F % 00 F (5) :7-- F F % a - a F % a - a 3 a - a + K K K F F F K F F % F K % 00 (3)
... 5-- 8--... :8-- 6.9 77.8 4.9 33 46.3 7.5 46 7.9 64.5 87.8 33.7 7 7.8 33.8 59. 8.8 80. 8.3 43.7 4.6 7. 64 58.3 37.9 7. 79.9 54.3 89.7 6.3.5 70. 67 5.5. 8.6 3.7 4.9 6.8 99. 0.3 0.5 8.3 99.3 4. 47 98. 0.3 44..7 66.3 3. 6. 67 39.6 39. 6.3.9 7. 67.5 64 93.7 5 40 0. 73.9 8. 5.4 4.5 67.3 6.4 5.4 35.9 6.5 83. 88 37.8 9. 80 45.4 73.8 73.9 63.8 54. 3. 53 5.3 63.6 46. 4.9 55.6 ( K 5) R Max Mn 99.3.3 99 R + L K 99 + 0 5. 9--. :9-- (4)
( ) 0 0 0 40 40 60 60 80 80 00 F 4 6 7 90 - F % 5.56 8.89 8.89 4.44. 00.... (). " ( < ) " ". ( ) ". : r 0 ( ) CF F r,,..., K, K + r (6). ( K +) F 0 0. CFr CFr % K r,,..., K, K + F ( ) (7) -- 0--.. :0-- (5)
< < < < K + a a a 3 a K < a a + L K CF CF 0 CF CF 3 CF K CF K + n :-- K + a a a 3 K K F CF F K K a K a a + L K K K F F CF CF 3 F CF K F CF K + 0 (Monotonc).. 6-- 5--. : 40 ( 60 ( 80 40 ( 60 ( 80 ( 60 0 ( (6)
- 9-- 3-- --. (.7) (.6).. 50 40 (. 3-- ) 57 60 ( (--- 39 80 40 ( (40) 40 (79) 80 () 80 (50) 40. :-- < 0 0 0 < 0 4 5.56 < 40 40 44.45 < 60 57 63.34 < 80 79 87.78 < 00 90 00 :3-- 0 90 00 0 76 84.44 40 50 55.55 60 33 36.66 80. 00 0 0 63.34% 60 (..% 80 (. (7)
60 0 ( 0 63.34 5.56 47.78 60 3- " ".................... (8)
-... SPSS SAS...... 30-3- ( ).( ). -3-30 :-3-55 4 6 5 3 49 36 37 5-3- -3-.. :. (9)
. -3-. 60 50 توزيع العينة حسب الجنس والمنطقة 55 49-3- عدد الطلاب 40 30 4 6 3 36 5 37 0 5 0 0 الجنوبية الغربية الشرقية الشمالية الوسطى طالبات طلاب عدد الطلاب توزيع العينة حسب الجنس والمنطقة 00% 90% 4 80% 5 36 5 70% 60% 50% 40% 55 6 30% 3 49 37 0% 0% 0% الوسطى الشمالية الشرقية الغربية الجنوبية -3- طالبات طلاب 3-3-.. (0)
- 37 طلاب 55 3-3- 49 3 6 الجنوبية الغربية الشرقية الشمالية الوسطى 5 طالبات 4 5 36 الجنوبية الغربية الشرقية الشمالية الوسطى -3- ( ) -3-44. :-3-5 3 5 7 6 5 9 9 0 3 5 6 40 33 7 34 6 8 39 9 0 47 35 5 38 3 53 4 55 45 0 ()
. 4-3-.. 60 50 40 30 0 0 4-3- 0 ذو الحجة ذو القعدة شوال رمضان شعبان رجب جمادى الثانية جمادى الاول ى ربيع الث اني ربيع الاول صفر محرم الارباح المبيع ات التكاليف 5-3-.. ()
- 60 50 40 30 0 0 الارباح التكاليف 5-3- 0 ذو الحجة ذو القعدة شوال رمضان شعبان رجب جمادى الثانية جمادى الاول ى ربيع الث اني ربيع الاول صفر محرم 3-3- (7-3- 6-3- ) 40-45 : 47 40-48 45 40 (3)
40 49 48 47 46 45 0 5 0 5 0 5 30 35 40 45 50 55 60 65 70 75 عدد السيارات المباعة (الف سيارة) 6-3- 45 40 اخرى اسيوي امریكي 00% 90% 80% 70% 60% 50% 40% 30% 0% 0% 0% 45 46 47 48 49 40 مستعمل جدید 7-3- 45 40 6-3- : 7-3-.. 67 47 6-3-. -48 49 48 33 6 : 40 40 9. 40. 40 49 48 (4)
- 49. 45 55% 40 57% 45 ( 4 )/4 4-...........( )... (5)
.... -4-.... :. (Mode) ( ).( )... ( ) :. (6)
-.. ( ). : * F. * F F,,..., K L (8). L F K.. ) F A ( F F. L F F M A + L F F F ( ) (9). F M A + L F + F ( ) (0).. : F F M A + L F F F F M A + L F + F ( ) ( ) F : (7)
F F A L : (Medan).. ( ) ( ).. [ n + ]. Q + n n (). : n n & + & n n + Q + n n + ().. (8)
- ( ) :. Q n ( ) Q + n n + ( n ) ( n ) + Q... K +F. K + F CF Q A + L CF CF. CF CF. ( ) A (3) L. : + F CF Q A + L CF CF ( ) CF CF : L A (9)
: (Arthmetc Average or Mean)... µ. N ( ) N µ N (4) n n n (5).. µ. µ µ (7-- ).. a + a +,,..., K (6). a + a ( ) :. N N µ N n (30)
- n n K K F F (7) --4-.( ) :--4- a - a a - a 3 ak - a K + K F F F F K F K F F F F K K K F : K K F F : F --4- --4-.. (3)
:--4-3 8 7 8 8 7 5 9 6 8 5 4 7 8 9 3--4-. :3--4-7 5 4 9 8 7 6 3 3 3 5 8 ( 5 ) 8 M 8.4--4-3 :4--4-6 7 7 8 8 8 8 8 9 4 5 5 7 9 N N & + + + Q 9 + 0. 0 µ ( 4). (3)
- 3 0.5 µ --4-3 5--4- :5--4-0 39 4 6 35 8 5 9 3 5 9 37. 4--4-. 5--4-0 :6--4-4 5 8 9 3 5 6 9 35 37 39 n + 3 + 4 7 Q 7 3.. 3 3 3 4 3 3 (33)
. 4 3--4-850 7--4-850 :7--4- () F 0-60 0-60 30-40 50-70 80-00 0 F 850. F * F. 8--4- :8--4- () F * F 0-60 6 0-60 8 30-40 50-70 9 80-00 0 6 F 850.. (34)
. L 0 F F - ( ) 9 8 & F 9 F F M A + L F F F ( ) 30 ( ) 8 30 + ( 0) 4.4 8 9 F M A + L F + F ( ) 9 30 + ( 0) 40.6 8 + 9 ( ) 0 4.4 40.6..(9--4- ) :9--4- CF < 0 0 < 0 60 < 30 0 < 50 460 < 80 730 < 00 850 + F 85 45.5 + F CF Q A + L CF CF ( ) ( ) 45.5 0 30 + ( 0) 47. 460 0 (35)
. 47.. 0--4- :0--4- () F F 0-60 5 300 0-60 0 300 30-40 40 9600 50-70 65 7550 80-00 0 90 0800 850 4450 K K F F ( 7) 4450 48.8 850. 48.8-4-....... (36)
-...........Q : (Quartle Devaton)... ( ) Q ( Q 3 ) Q Q Q 3 (8).. (37)
... : ( n + ) 4 : ( n + ) 3 4 Q + n 4 (9) Q + 3 3( n ) 4 (0)... 35.7 35.7 + 35 36 Q Q Q 3 ( ) : : Q Q + n 4 (38)
- : Q 3 Q + 3 ( n ) 3 4 ( 8).. ( + F ) 4 ( + F ) 3 4 CF L A.CF ( + F ) CF Q 4 A + L CF CF ( ) () ( + F ) 3 CF Q 4 3 A + L CF CF ( ) () Q Q Q 3 : + F CF Q 4 A + L CF CF ( ) (39)
( + F ) 3 CF Q 4 3 A + L CF CF ( ) : Mean. MD Devaton. ( ) n ( ) 0. N N µ MD P N N MD P N µ N. (3). MD n n MD n n (4) (40)
- ( ) : N MD P N N µ n MD n n µ... MD K ( F ) K F (5). MD K ( F ) K F : K (4)
:. σ. S. σ σ or S S. N N σ ( ) µ N N σ µ N (6) n S n ( ) n S n n n (7) ( ) : N N σ µ N n (4)
- S n n n ( 6) ( 7) N σ µ N S n n n (8) (9) ( ) : N N σ µ N n S n n n ( ). σ σ.. S K ( ) F K F : S K ( ) K F F K F (30) (43)
: S K ( ) K F F K F K S K ( ) K F F K F (3) : S K ( ) K F F K F K --4-. --4-. Q 3 Q.. Q + N 4 (4--4- ) + 5.75 4 --4- (44)
5 + 6 8 + 8 8 Q + 3 3( N ) 4 3( + ) 7.5 4-7 + 8 + 4 3 Q3 Q Q 3 8.5 3 µ 0.545 N µ 8 0.545 + 0.545 +...... + 0.545 + 3 0.545 70 N µ x 70 MD p 3.8 N ( µ ) ( ) ( ) 8 0.545 + 0.545 +... ( ) ( )... + 0.545 + 3 0.545 349.4545 ( µ ) σ N 349.4545 5.8849545 3.9855 ( µ ) σ N 349.4545 5.8849545 (45)
--4-.. Q Q Q + n 4 3 + 4 Q 3 --4-3.5 3 + 4 5 + 8 6.5 Q + 3 3( n ) 4 + 3( 3 ) 4 0.5 0 + 9 + 35 3 3 6.5 Q 7.75 3 3 3 3 4 3 0 4 + 4 4 +...... + 37 4 + 39 4 94 (46)
- 3 n 94 MD 7.3 n 3 ( ) ( ) ( ) 37 4 + 4 +... ( ) ( )... + 39 4 + 0 4 988 S S ( ) n 988 8.33 9.074 3 ( ) n 988 8.33 3--4-3--4-.7--4- (9--4- ) ( F ).Q 3 Q + + 850.75 4 4 () ( + F ) CF Q 4 A + L CF CF.75 60 0 + ( 0) 9. 0 60 ( ) :9--4- CF (47)
< 0 < 0 < 30 < 50 < 80 < 00 0 60 0 460 730 850 ( + F ) ( + ) 3 3 850 638.5 4 4 () ( + F ) 3 CF Q 4 3 A + L CF CF 638.5 460 50 + ( 30) 69.8 730 460 Q3 Q Q 69.8 9. 0.35.(--4- ) F 48.8 F ( ). () 0-0 - 30-50 - 80-00 :--4- F 60 60 40 70 0 850 5 0 40 65 90 F 300 300 9600 7550 0800 4450 ( ) -43.8-8.8-8.8 6. 4. 43.8 8.8 8.8 6. 4. F 68 4608 4374 4944 8666 MD ( F ) F (48)
- 8666.96 850.(--4- ) () 0-0 - 30-50 - 80-00 :--4- F 60 60 40 70 0 850 5 0 40 65 90 F 300 300 9600 7550 0800 4450 F 500 64000 384000 40750 97000 5650 ( ) 98.44 89.44 77.44 6.44 697.44 ( ) F 506.4 370.4 8585.6 70858.8 0369.8 540954. 48.8 S K ( ) K F F K F 4450 5650 ( 850) 850 850 S 637.6 5.4 ( ) ( F ) F 540954 637.66 5.4 849. S 637.6.. (49)
. 90 48 (A ). ( ) 53 5 45 (B ) µ µ 50 A B σ 06 & σ.7 A B B A..B A.. ( Y ) ( ) ( 5 ) 3.8 & 5.6 S.9 & 3. Y S Y..9 3.8 S 5.6. S 3.. Y. 4--4- (50)
-. 00 300 Y Y 35 & S 5 33 & SY. 5--4-. S 5 S. :.... : Y σ CV p 00 µ (3) (5)
. CV S 00 (3). ( ) CV p σ 00 µ CV S 00 6--4-... Y : Y 7.8 & S 0.5 300 & SY 50000.. CV S ( ) 00 (5)
- 0.5 00 4.5% 7.8. : CV Y S Y ( ) 00 Y 50000 00 5.6% 300 4.5%.5.6%. 5-..... -5-. (53)
.. 00% S. S {,,3,4,5,6 }. E ( ) 0 Pr E,,..., n (33) 00%. n n ( S ) ( E ) Pr Pr (34) A () A S A S (35) S A A {,4,6} ( A ) 0 Pr A (36) -5-. A. (54)
-. ( ) ( j ) Pr A Pr E E A j A (37) (.35 ) ( A ) ( S ) Pr Pr (38). n ( S ) A A Pr A ( A ) A ( ) ( ) n A n S n ( A ) (39) ' A A : A. S ' ( A ) ( A ) Pr Pr (40) ' ( A ) ( A ) ( S ) Pr + Pr Pr (4) --5- A 6. A S. S {,,3,4,5,6 } Pr ( E ) E,,3, 4,5,6 6 A A {,4,6} ( ) ( ) n A 3 Pr( A ) 0.50 n S 6 (55)
4 5 3... 4 S {.,.,.3,.,.,.3,.4,.5,3.,3.,3.3,3.4, 4., 4.} E. 3.. Pr ( E ) 4 A A { 3.,3.,3.3,3.4 } Pr ( A ) 4 ( ) ( ) n A 4 n S 4 A --5-.. ( ). (56)
-... --5-3--5-476 :--5-50 356 406 35 63 56 385.. --5-... :--5- Pr 0. 0.07 0.09 (57)
Pr 0.05 0.3 0.6 0.9 ( ) % ( ) 7%. 3-5-. S B A A S & B S. C C A B D D A B -3-5-. B A. ' S. ' S (58)
- B A B A -3-5- A B S A B.(Mutually Exclusve) A A '. A -3-5- S {, 3, 5, 7, 9,,3,5,7 } : : A { 5, 9,3,7} B { 3, 5, 7,5,7} C {,3,7 } A A ' C B ' (c (f A C ( A B ) ' A B C (b (e (h ' A ' A B A B C (a (d (g A C ' A {,3, 7,,5} {,3,5,7,9,3,7 } (a (b (59)
A ' ' A B A B ' B A C {, 3, 5, 7,,5,7 } ( A B ) ' A ' B ' {,} ' ( ) {, 3, 7, 9,,3,5 } A B C {,3, 5, 7, 9,3,5,7} A B C (c (d (e (f (g (h ( ) ' ' ' A B A B ( ) ' ' ' A B A B. ( A ) ( A ' ) Pr + Pr (4) : Pr( ) 0 (43) Pr ( ) Pr ( S ' ) Pr( S ) B A A 0 S B ( A ) ( A B ) + ( A B ' ) Pr Pr Pr B (44) A B ( B ) ( B A ) + ( B A ' ) Pr Pr Pr (45) ( A B ) ( A ) + ( B ) ( A B ) Pr Pr Pr Pr (46) (60)
- ( A B ) Pr 0 (47) ( A B ) ( A ) + ( B ) Pr Pr Pr (48) : S {,3,5, 7,9,,3,5,7 }.( ) A { 5,9,3,7} B { 3,5,7,5,7 } C {,3,7 } ( C ) Pr A ' ' ( B ) Pr A (c (f ( C ) Pr A ( B ) ' Pr A ( ) Pr A B C (h (b (e : Pr ( A ' ) ' ( B ) Pr A -3-5- ( ) Pr A B C (a (d (g Pr 7 (b 9 ( A C ) Pr Pr Pr ( ) A 9 ( A C ) ' 5 Pr 0 Pr ( A B ) 9 ' 7 ( A B ) Pr( A B ) ' ' ' 9 ( A B ) Pr( A B ) ' 9 8 Pr( A B C ) 9 ' ' 7 ( A B C ) Pr 0 (a (c (d (e (f (g (h 3-3-5- S B A Pr ( A ) 0.6 Pr ( B ) 0.7 ( A B ) Pr 0.3 (6)
( B ) ' Pr A ' ( B ) ' ' ( B ) Pr A Pr A (b (d (f Pr ( B ' ) ( B ) Pr A ( B ) ' Pr A (a (c (e ' ( B ) ( B ) Pr Pr 0.7 0.3 (a ' ( A B ) ( A B ) Pr Pr (b 0.3 0.7 ( A B ) ( A ) + ( B ) ( A B ) Pr Pr Pr Pr (c 0.6 + 0.7 0.3.0 ( A ' B ) ( A ' ) + ( B ) ( A ' B ) ' Pr( A ) + Pr( B ) Pr( B ) Pr( A B ) ' Pr( A ) + Pr( A B ) Pr Pr Pr Pr ( B ) Pr 0.7 (d ' ( A B ) ( A B ) Pr Pr 0 (e Pr ' ' ( A B ) Pr( A B ) ' ( A B ) Pr 0.3 0.7 (f 4-5-. Pr ( A B ) : B A ( A B ) ( B ) Pr Pr (49) (6)
- ( A B ) ( A ) ( B ) Pr Pr Pr (50) ( A B ) ( A ) ( B A ) Pr Pr Pr (5) ( A B ) ( B ) ( A B ) Pr Pr Pr (5). r S S A A A r A A j j r ( A ) Pr D (53) ( ) Pr D A,,..., r (54) D A ( ) ( ) ( ) Pr A D Pr A Pr D A,,..., r (55) D Pr ( D A ) Pr ( A ) Pr r ( D ) Pr( A D ) r ( A ) ( D A ) Pr Pr (56) D A ( A D ) Pr Pr ( A D ) Pr( D ) (57) (.57) (63)
( A D ) Pr ( A ) ( D A ) Pr Pr r Pr( A ) Pr ( D A ) (58). A 4 0.09 0.06 A 3 A A : Pr( A ) 0.0 & Pr ( A ) 0.30 Pr( A ) 0.40 & Pr( A ) 0.0 0.07 3 4 0.05-4-5-. A 3 Pr ( D A) 0.05 & Pr ( D A ) 0.07 Pr ( D A ) 0.06 & Pr ( D A ) 0.09 3 4 ( ) Pr D ( A D ) Pr 3 4 ( D ) ( A D ) Pr Pr ( A D ) ( A ) ( D A ) 0.0( 0.05) 0.0 Pr Pr Pr ( A D ) ( A ) ( D A ) ( ) Pr Pr Pr 0.30 0.07 0.0 ( A3 D ) ( A3 ) ( D A3 ) ( ) Pr Pr Pr 0.40 0.06 0.04 ( A4 D ) ( A4 ) ( D A4 ) ( ) Pr Pr Pr 0.0 0.09 0.009 Pr( D ) 0.0+ 0.0+ 0.04 + 0.009 0.064 ( D ) Pr A 3 (64)
( A D ) Pr 3 4 ( A ) ( D A ) Pr 3 Pr 3 Pr( A ) Pr ( D A ) 0.04 0.375 0.064-55% MSCE 30%. 0% A Pr( A ) 0.0 ( ' ) Pr A 0.80 : Pr ( D A ) 0.30 ( ' ) Pr D A 0.55 ' A D -4-5- ( D ) ( D A ) + ( D A ' ) ' ' Pr( A ) Pr ( D A ) + Pr ( A ) Pr ( D A ) Pr Pr Pr 0.0( 0.3) + 0.80( 0.55) 0.06 + 0.44 0.50 : ( A D ) Pr Pr ( A D ) Pr( D ) Pr ( A ) Pr ( D A ) Pr Pr Pr Pr ' ' ( A ) ( D A ) + ( A ) ( D A ) 0.06 0. 0.50 (65)
R Max Mn ( ) F F M A + L F F F ( ) ( ) F M A + L F + F ( ) n ( ) : ( ) Q + n n + ( n ) ( n ) + Q + F CF Q A + L CF CF ( ) : ( ) : N N µ N n (66)
- n n : K K F F ( ) : Q + Q Q 3 ( n ) 3 4 Q 3 Q + n 4 : Q3 Q Q + F CF Q 4 A + L CF CF ( + F ) ( ) 3 CF Q 4 3 A + L CF CF ( ) ( ) : N MD P N N µ n MD n n : (67)
MD K ( F ) K F ( ) : N N σ µ N n S n n n ( ) : N N σ µ N n S n n n : S K ( ) K F F K F : S K ( ) K F F K F (68)
- CV p σ 00 µ S CV 00 (69)
. 54 ( ) - 8 - - 0-30 4 6 ( : ( ) 50 ( ( ) - 5-9 - 3-7 8 0 0 :. 5 (3 0-4 - 8 - - 6 8 9 3 -: (70)
- 60% 5% 0% 5% (4 (D C B A) 5% 3% 7% 0%.. D C B A.(D) (5 0 8 6 9 4 0 7 -: (6 Pr ( A ) 0.50 ' ( ) Pr B A 0.60 ( B ) Pr A (7 0.8. (8 4 00 6 38 00.. (7)
(9 3 4 5 6 7 8 9 3 7 0 4 9 6 8 0 -: (0 38 8 - - 6-0 - 4-8 3 6 4 0 5 38 -: ( Y : 380 & S 84 Y 89 & S 5 x y ( ) ( ( ) 5 9 7 5 8 (7)
- 34 9 35 9 9 6 6-8 - - 0-30 - 50 (3 50 4 8 0 6 : 45 33 7 4 4 5 4 (4 (5 0 6 8 0 4 3 : (6 (73)
8 74 90 80 70 80 64 70 60 40 ( ) 0-40 - 00-00 - 300 0 7 (7 : 00 9 0 36 (8 : (9 5 7 4 6 7 4 9 8 8 4 9 4 4 34 4 5 6 3 9 0 5 7 0 4 6 4 7 6 3 3 7 5 9 (74)
- 7 0-0 - 5-0 - 5-40 4 9 6 30 (0 00 0 37 0 7 5 ( ( ) 4 ( (75)
- 6-0 - 4-8 3 8 7 4 : 7 0 3 5 4 5 (3 : (4 0 5 8 4 7 0 3 6 9 7. (5.. (76)
- 00% 50% 0% الشهر اجمالي اعداد الملتحقين في الدورات الاداریة في المعهد جماد اول ربيع ثاني ربيع اول صفر الشهر محرم 0 00 00 300 400 500 600 700 800 900 000 00 00 300 اعداد الملتحقين (6 80. 5 التكرار الصاعد المنحنى التكراري المتجمع الصاعد 80 80 7 64 65 56 48 40 3 37 4 6 8 0 <5 <0 <5 <0 <5 حدود الفي ات الصاعدة : (77)
. 40% 8 7 (7 48 ( ) 0-0 - 30 30-70 70-00 00-50 5 8 6 7 : ( ) 6. 48. 3.4 (8 0% 30% 5% 0% :.. % (9 4 () ().3 (78)
3 4 5 6 7 8 9 0 3 4 0 36 0 5 0 0 4 5 3 6 45 9-5.6 9.4.8 3. 5.6 4.9 3. 6 7.5 3. 6. 9.6 : 0.0 0.30. 0.50 0.0 : () :. 0.4 0.6.. (30 6.5 -.5-5.5-8.5-0.5 -.5 3 6 7 3 60 (3 : (79)
( ) 0-0 - 30-40 - 50 0 3 5 (3 800 0-50 - 70-00 - 00 44 3 84 340 (33 (34 0 9 9 8 0 9 0 0 8 3 9 3 9 4 0 3 3 0 (35 (80)
- ( ) ( ) ( ) Pr A 0.0 & Pr B A 0.50 & Pr A B 0.4 ( B ) Pr A ( A ) ( B ) ( ) Pr 0.0 & Pr 0.30 & Pr A B 0.5 (36 : Pr( A B ) Pr ( B A ) (37 ( A B ) ( B ) ( A ) Pr 0.65 & Pr 0.30 & Pr 0.50 ( B ) Pr A (38 : ( Y ) 3 3 6 4 5 3 7 4 ( ) 6 7 6 7 7 8 9 8 7 6 6 9 8 7 : Y ( ) Y (39 (8)
( A ) ( B ) ( A B ) Pr 0.40 & Pr 0.30 & Pr 0.58 B A 0-0 - 30-40 - 50 34 8 9 5 (40 (4 : 6 66 48 59 6 57 45 4 66 45 53 4 40 55 67 65 45 45 65 : ( ) 0-30 - 40-50 - 60-70 (4 78 6 5 36 7 4 78 60% (8)
- 45 (43 ( A B ) ( A ) Pr 0.5 & Pr 0.50 ( B A ) Pr (83)
(84)
- -.. :. 6.0.75 6.. 6 8... 8 6. 0.3 6 0.68. ( 6 ) 8 6 0.97. (85)
. -... 36. (--). 6 (86) :-- 6 6, 6, 6,3 6,4 6,5 6,6 5 5, 5, 5,3 5,4 5,5 5,6 4 4, 4, 4,3 4,4 4,5 4,6 3 3, 3, 3,3 3,4 3,5 3,6,,,3,4,5,6,,,3,4,5,6. 36 (--). 36. 0,,,3, 4,5 3 4 5 6 : ( ) ( 6 ) 5
- (--).. 6 5 4 3 0 ( ) :-- 5 4 3 4 3 0 3 0 0 3 0 3 4 0 3 4 5 3 4 5 6. (--) : 6 Pr ( 0) 36. 0 Pr ( ) 36 8 Pr ( ) 36 6 Pr ( 3) 36 4 Pr ( 4) 36 Pr ( 5) 36 : :,3,4,5,6,7,8,9,0,,. ( ). :. (87)
....... --..... 70 70..... --.. (88)
-... ( ) ( x ) 0 Pr. Pr x x ( x ) Pr. f ( x ) 0 : : f.( ) :. (--) ( ) f x. (89)
(x) f ( ) -- 3-... : ( ) Pr ( ) E x x x () x. E ( ). 5 ( ) Pr ( ) E x x x 0 6 0 8 0 + + 36 36 36 6 4 8 3 + 4 + 5 36 36 36.94 : (90)
-..94. : ) () µ.(. ( ) σ ( ). ( ) Pr ( ) µ E x x x () ( x ) Pr ( x ) σ µ x (3) : x Pr ( x ) σ µ : x (4) σ σ x Pr ( x ) µ x (5). 0 (9).... -3-
(9) :. : 0.5 0 0.5 Pr ( ) ( ) Pr ( ) µ E x x x 0 0( 0.5) + ( 0.5) 0.5 ( x Pr ( x )) x 0 0 ( 0.5) ( 0.5) ( 0.5) σ µ + 0.5 σ σ 0.5 0.5. 8 6 0 3.. : 0,,,3..... -3-
- (-3-).( ). 0/4 9/3 4/3 8/ 3 4/ 9/ 3/ 0.05989 0.03755 0.03755 0.49868-3- 0 8 4/4 0/3 3/3 9/ 3/ 0/ / 0 0.03755 0.49868 0.49868 0.7984 6. ( ). : 0 3 ( x ) Pr 0.7984 0.449604 0.365 0.05989.000000 : 3 ( ) Pr ( ) µ E x x x 0 ( ) ( ) ( 0.365) 3( 0.05989) 0 0.7984 + 0.449604 + +.5000 3 x Pr ( x ) σ µ x 0 (93)
( ) ( ) + 0 0.7984 0.449604 ( ) ( ) + 0.365 + 3 0.05989.5000.865.56505 0.665765 σ σ 0.665765 0.85947-3-.. (5) (4) (). -3-.. (-3-) 8.. 8 56 56. 5 3768 5.. -3-. : : (94)
-. :.... :.. -3-...... n : 0,,,3,..., n : n Pr x x ( ) ( ) ( n x x P P ) (6)... ( p ) n x P (95)
n n x x :. n n! x x! ( n x )! (7) n n! ( )( ) n! n n n.... n x ( x ) :. P n. ( ) ~ Bn n, P Pr P n. --3-. 0. :. (. ( : ( : () ( ( ) ( ) (0.90) (0.0) (... 0.0 P : 0,,,3,4,5,6,7,8,9,0, : (96)
( ) ~ Bn, 0.0 - : ( Pr ( ) ( 0.0) ( 0.0)! 0.0 0.90!! 0 ( ) ( ) ( ) ( ) ( ) 0.0 0 ( ( ) ( ) ( ) ( ) Pr 0 Pr 0 + Pr + Pr + ( ) ( ) ( ) ( ) ( ) ( ) Pr 3 + Pr 4 + Pr 5 + Pr 6 + Pr 7 + Pr 8 + ( ) + ( ) Pr 9 Pr 0 x 0 ( ) ( ) Pr 0 Pr ( x ) Pr 0.0 0.0 0 : ( ) ( ).. : ( ) µ E np (8) (97)
( p ) σ np (9) σ np ( P ) (0) P 0.0 n : ( ) np ( ) ( P ) ( )( ) µ E 0.0. σ np 0.0 0.90 0.99 ( P ) σ np 0.99 0.995 --3-. 75 00 : 8. (. (.6 ( (. :. (. ( ( 3.0.75. P 0.75 (98)
( ) ~ Bn 8, 0.75 - P 0.75 n 8. ( 8 8 8 8 Pr ( 8) ( 0.75) ( 0.75) 0.00 8 8 ( ( ) ( ) + ( ) + ( ) Pr 6 Pr 6 Pr 7 Pr 8 8 8 + 6 7 8 8 8 8 + ( 0.75 ) ( 0.75 ) 8 ( 0.75) ( 0.75) ( 0.75) ( 0.75) 6 8 6 7 8 7 0.458 + 0.6697 + 0.00 0.4966 6 6 ( ( < ) ( ) + ( ) Pr Pr Pr 0 8 8 + 0 ( 0.75) ( 0.75) ( 0.75) ( 0.75) 7 0 8 0.00037 + 0.0000 0.00039 ( ) np ( ) µ E 8 0.75 6 σ np ( ( p ) ( )( ) 8 0.75 0.75.5 ( p ) σ np.5. -3-. : (99)
( ) (00) ()...... () (3) : ( ) ~ Po λ. λ. ( )....... λ :........ ( ) ~ Po λ. λ.
-. n (, ) Bn n p. P n n.. Pr ( x ) λ x e λ x! () :... 0 x λ.78883 ( )( ) x! x x x x e x! --3-. 5 :. 6 (. 3 (. (0)
. λ 5 λ 5 ( ). : ( ) Pr 6 e 6! 6 λ λ ( ) 6 5 5 e 6! ( 5) (.78883) 6 5 0.463 6 5 4 3 :.! Exp e ( ).. ( x < ) ( ) + ( ) + ( ) Pr 3 Pr 0 Pr Pr 5 e 5 e 5 e + + 0!!! 0 5 5 5 0 5 5 e 5 5 + + 0.465 0! --3-. :. (.3 (. ( (0)
- λ : ( 0 e Pr ( 0) 0.35335 0! (..... 0 ( ) ( < ) Pr 3 Pr 3 ( ) ( ) ( ) Pr + Pr + Pr 0 e e e + +!! 0! 0 0 e + + 0! 0.676676 0.3334 e Pr ( ) 0.7067! ( : ( ) µ E λ () σ λ (3) σ λ (4) ( n > 00) n (03)
. ( P < 0.05) ( ). λ ( ) λ E np (5) 3--3-. 000 5 000 0.000 : 000.. ( ) ~ Bn 000.0.000 : 5 ( < ) ( ) + ( ) + ( ) + Pr ( ) + Pr ( 0) Pr 5 Pr 4 Pr 3 Pr 000 4 000 4 ( 0.000 ) ( 0.9998 ) + 4 000 3 000 3 ( 0.000 ) ( 0.9998 ) + 3 000 000 ( 0.000 ) ( 0.9998 ) + 000 000 ( 0.000 ) ( 0.9998 ) + 000 0 000 0 ( 0.000 ) ( 0.9998 ) 0 0.0000543 + 0.000890 + 0.063645 + 0.637756 + 0.88744 0.9999978 (04)
-. p < 0.05 n > 00 Pr( 5) ( ) λ np 000 0.000 0. 4 < x 0 x e x! λ λ ( 0.) ( 0.) ( 0.) 0 0. 0. 0. e e e + + 0!!! ( 0.) e ( 0.) : : 3 0. 4 0. e + + 3! 4! ( ) 0 0. 3 4 0. 0. 0. 0. 0. e + + + + 0!! 3! 4! 0.887308(.4) 0.9999978 ( n > 00).. ( P < 0.05). 00 60 000 60 000 60 Pr ( 60) ( 0.000) ( 0.9998) 60 000 999 998 94 0.000 0.9998 60 59 58 ( ) Pr 60 ( ) ( ) : 60 000 60 : ( ) 60 0. 0. e 60 : 000 99.0 60! (05)
4-. 3....... ( ).. 70 70.. 00 00 76. 00.... 00 ( ) Pr 0 < < 00. 80 60 0. 00 : 8 (06)
- ( < < ) Pr 0 60 ( < < ) Pr 80 8 : -4-.(-4-) :. (. (. ( -4-4 3 (. 0.5.. (07)
(.. (.0.50 4.0.50.. (). f ( ). ( a, b ).b. b a a.(-4-) f ( ). ( ) Pr ( a < < b ) f x dx b a : b a.. (08)
- (x) f ( ) -4- ) ( a b -4-...σ µ ( : µ, σ ) x µ σ f x e πσ (6) σ > 0 < µ < π 3.4596 < : < e.788885..(--4-) µ 0.5 µ.. (09)
f ( ) --4- µ µ.. σ.(--4-) σ... --4-0.0 N(30,5) N(80,00) N(0,4) 0.6 0. 0.08 0.04 0.00 0 0 40 60 80 00 0 40 (0)
-. µ 68.6%. σ.σ µ ( µ σ ) ( µ + σ ) : (3--4-) 68.6% ( µ σ ) ( µ + σ ) 95.45% ( µ σ ) ( µ + σ ) 99.73% ( µ 3σ ) ( µ + 3σ ) ( ( (3 µ ( ) ~ N µ, σ : σ σ µ. 68.6% 3--4- µ σ 95.45% 99.73% ( µ 3σ ) ( µ σ ) ( µ σ ) µ ( µ + σ ) ( µ + σ ) ( µ + 3σ ) µ Z. ()
Z. Z ( ) ~ N 0, f ( Z ) e π Z (7) π 3.4596 < Z : < e.788885 --4- Z ( ) ~ N 0, Z : Pr ( < Z < ) ( Pr ( < Z < ) ( ( < Z < ) Pr 3 3 ( (3--4-) : ( Pr( < Z < ) Pr (( 0 ) < Z < ( 0 + ) ) Pr (( µ σ ) < Z < ( µ σ )) 0.686 ( < Z < ) P r (( ) < Z < ( + )) Pr (( µ σ ) < Z < ( µ + σ )) Pr 0 0 0.9545 ( < Z < ) (( ) < Z < ( + )) Pr 3 3 Pr 0 3 0 3 ( ( ()
(( µ σ ) Z ( µ σ )) Pr 3 < < + 3-0.9973 Z b Pr ( ) ( ) a < < b f x dx a (8). Z. Z : φ ( ) ( ) φ a Pr < Z < a a 0 --4-.39 Z Pr ( Z <.39) φ (.39) (3).( ) Z.3.0.09 Z.0.977.39 ( ) ( Z ) φ.39 Pr <.39 0.977 : ( ) a ( ) ( ) φ a f Z dz
. ( b a a 0 ). ( Z > a) φ ( a) Pr ( < < ) φ ( ) φ ( ) Pr a Z b b a ( Z < a) φ ( a) Pr Pr ( Z > a) φ ( a) ( a Z b ) φ ( a) φ ( b ) Pr < < + ( < < ) φ ( ) φ ( ) Pr b Z a b a (9) (0) () () (3) (4) Pr ( Z > a) Pr ( a < Z < ). Pr ( < Z < a) φ ( a) (9) : (0) : ( a < Z < b ) ( < Z < b ) ( < Z < a) Pr Pr Pr ( b ) φ ( a) φ () : Pr ( Z < a) Pr ( < Z < a ) ( Z ) Pr a < < Pr ( < Z < a) φ ( a) () : Pr ( Z > a) Pr ( a < Z < ) Pr ( < Z < a) Pr ( a < Z < ) Pr ( < Z < a) + Pr ( < Z < a) Pr ( < Z < a) φ ( a) (4)
- (3) : ( a < Z < b ) ( < Z < b ) ( < Z < a) Pr Pr Pr ( Z b ) Pr ( a Z ) Pr < < < < ( Z b ) ( Z a) Pr < < Pr < < ( Z b ) ( Z a) Pr < < + Pr < < ( Z b ) ( Z a) Pr < < + Pr < < ( b ) φ ( a) φ + (4) : ( b < Z < a) ( < Z < a ) ( < Z < b ) Pr Pr Pr ( a Z ) Pr ( b Z ) ( Z a) ( Z b ) Pr < < < < Pr < < Pr < < ( Z a) ( Z b ) Pr < < + Pr < < ( Z b ) Pr ( Z a) Pr < < < < ( b ) φ ( a) φ 3--4- : ( < Z < ) Pr.39 0 Z ( < Z < ) ( Z < ) ( Z < ) φ ( 0) ( φ (.39) ) Pr.39 0 Pr 0 Pr.39 4--4-0.98. Z ( < Z < ) Pr 0.98. Z. ().(4--4-) : (5)
( < Z < ) ( Z < ) ( Z < ) Pr 0.98. Pr. Pr 0.98. φ (.) φ ( 0.98) φ (.) ( φ ( 0.98) ) 0.8686 ( 0.8365) 0.8686 0.635 0.705 Z 70.5%. 0.98 0.4 0.3 0. 4--4- (-0.98.) 0. 0.0 0.98 µ 0. Z 5--4- Z ( ) ~ N 0, : Pr ( 0.07 < Z <.08) ( Pr (.75 < Z < 0.75) ( (4) (0) (6) : ( 0.07,.08) ( < Z < ) ( Z < ) ( Z < ) Pr 0.07.08 Pr.08 Pr 0.07 Z : (5--4-). [(0) ] ( < Z < ) ( Z < ) ( Z < ) Pr 0.07.08 Pr.08 Pr 0.07 (
(.08) φ ( 0.07) φ 0.98 0.579-0.4533 Z (6--4-) ( (4).(-.75-0.75 ) :. ( < Z < ) φ ( ) φ ( ) Pr.75 0.75.75 0.75 0.9599 0.7734 0.865 0.4 0.3 0. 5--4-.05) (0.07 0. 0.0 0.07.08 Z 0.4 0.3 0. 0. 6--4-0.75.75 -.75 0.75 0.0 -.75-0.75 0.75.75 Z 6--4- Z ( ) ~ N 0, : Pr ( Z <.8) ( (7)
Pr ( Z >.8) Pr ( Z <.8) Pr ( Z >.8) ( (3 (4 ( Z < ) φ ( ) Pr.8.8 0.964 ( 0.4 0.3 0. 0. 0.0 ( Z > ) φ ( ) Pr.8.8 0.964 0.0359.8 Z ( 0.4 0.3 0. 0. 0.0 ( Z < ) φ ( ) Pr.8.8 0.964 0.0359 0.8 Z (3 (8)
- 0.4 0.3 0. 0. 0.0 -.8 0 Z (4 ( Z > ) φ ( ) Pr.8.8 0.964 0.4 0.3 0. 0. Z (9) -.8 0 Z. Z. Z σ µ. : :(8 ) 0.0 ( a, b ) b Pr ( ) ( ) a a < < b f dx.
b a e πσ x µ σ dx. σ µ. Z Z σ µ. ) Z : ( Z µ σ (5). Z µ σ σ µ ( a, b ) (7--4-). Pr < < a µ µ b µ Pr < < σ σ σ a µ b µ Pr < Z < σ σ ( a b ). Z σ µ b a a µ b µ, σ σ. µ σ. (0)
- 7--4- Z µ a b 0 ( a µ ) / σ ( b µ ) / σ Z 800 ( ) ~ N 800, (50) 50. 7--4- :. 950. 00. 770 850 950 ( : µ 950 µ Pr ( > 950) Pr > σ σ 950 800 Pr Z > 50 Pr ( Z > ) φ ( ) ( ( (3 0.843 0.587. (8--4-) ()
8--4-950 µ x 800 950 µ z 0 Z 00 () µ 00 µ Pr ( < 00) Pr < σ σ 00 800 Pr Z < 50 ( Z ) Pr <.6 φ (.6) ( : 0.996 : 770 850 770 µ µ 850 µ Pr < < Pr 770 < < 850 σ σ σ 770 800 850 800 Pr < Z < 50 50 30 50 Pr < Z < 0 50 ( Z ) Pr 0.0 < < 0.33 ( ) φ ( ) φ 0.0 + 0.33 0.5793 + 0.693 0.086 (3 ( ) ()
- ( ) Pr ( ) E x x x σ σ x Pr ( x ) µ x x Pr ( x ) σ µ x n Pr x x ( ) ( ) ( n x x P P )... ( P ) n x P ( ) µ E np ( p ) σ np σ np ( P ) (3)
Pr ( x ) λ x e λ x! : x 0,,,... λ.78883 ( )( ) x! x x x x e x! ( ) µ E λ σ λ σ λ ( : µ, σ ) x µ σ f x e πσ σ > 0 < µ < π 3.4596 < < e.788885 a ( ) ( ) φ a f Z dz (4)
- ( : ( ( ). (3 0.03 : 0 () : (4 Pr ( ) Pr ( ) Pr ( ) 0.5 6 0. - 8 0.5 7 0.4-3 4 0 0.5 8 0.3-4 8 0.5 9 0. -5 3 8 0.5 0 (5 0.5 : 5 (5)
4 : : 0.0 500 :. 3 4 4 4 (6 (7 (8 (9 σ.6 µ P n : 5 3 3 (0 (6)
- 49 600 : 68 60 587 5% 604 ( 5.4 75 ( : 0% 5% 50% 5 7 (3 : 0 70 80 70 8 75 68 ~N(0.,0.6) (4 : 0.6 0. 0.7.. 8 45 40 (5 (7)
(6. 8 57 ~ N (57,8) : : 48 68 50 73 48 (7 5. 83 55. 90 (8. 00 7 0 8 30 5 (9 8 58 400 80 4 485 9 (0.. (8)
- 8.5 8000. 8 Z µ σ σ µ σ z µ z (. (.. 4. 0.04 (3.8 3. 000 4000 0000 000 0000 4 (4 (5 8 5 (6 Pr ( ) 0. 0. 3 0. 4 0. 5 0.5 σ ( Y ) 3 E ( Y ) 3 Y (7. 7 0 Y (9)
. P 0.4 (8 n 0. 4 (9 ( ) ~ N,9 Pr( > 0) ( < < ) Pr 0 5 (30 ( ) ~ Po 3. Pr( > ) E ( 4 7) 8 74 60. (3 60. 0% (3. 7 3 0 0 (33 (30)
- 0 30 7 0.07 (34 ( ( ) ) Pr ( ) 8 0.0 6 0.40 5 0.0 3 0.30 E ( ) E ( 4 + 5) E ( ) (35.5 :. 7.8. 6. 5. 6.5 3. 0.6 (36 (37 0.6 5. 5 4 4 (38 8 5 (3)
. 0% (39 8 4 4 8 (40 4 8 50 0.0 : ( ) (4 (3)
- (33) Z : ( ) 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.0 0.0 0.00 Z 0.5359 0.539 0.579 0.539 0.599 0.560 0.50 0.5080 0.5040 0.5000 0.0 0.5753 0.574 0.5675 0.5636 0.5596 0.5557 0.557 0.5478 0.5438 0.5398 0. 0.64 0.603 0.6064 0.606 0.5987 0.5948 0.590 0.587 0.583 0.5793 0. 0.657 0.6480 0.6443 0.6406 0.6368 0.633 0.693 0.655 0.67 0.679 0.3 0.6879 0.6844 0.6808 0.677 0.6736 0.6700 0.6664 0.668 0.659 0.6554 0.4 0.74 0.790 0.757 0.73 0.7088 0.7054 0.709 0.6985 0.6950 0.695 0.5 0.7549 0.757 0.7486 0.7454 0.74 0.7389 0.7357 0.734 0.79 0.757 0.6 0.785 0.783 0.7794 0.7764 0.7734 0.7704 0.7673 0.764 0.76 0.7580 0.7 0.833 0.806 0.8079 0.805 0.803 0.7995 0.7967 0.7939 0.790 0.788 0.8 0.8389 0.8365 0.8340 0.835 0.889 0.864 0.838 0.8 0.886 0.859 0.9 0.86 0.8599 0.8577 0.8554 0.853 0.8508 0.8485 0.846 0.8438 0.843.0 0.8830 0.880 0.8790 0.8770 0.8749 0.879 0.8708 0.8686 0.8665 0.8643. 0.905 0.8997 0.8980 0.896 0.8944 0.895 0.8907 0.8888 0.8869 0.8849. 0.977 0.96 0.947 0.93 0.95 0.9099 0.908 0.9066 0.9049 0.903.3 0.939 0.9306 0.99 0.979 0.965 0.95 0.936 0.9 0.907 0.99.4 0.944 0.949 0.948 0.9406 0.9394 0.938 0.9370 0.9357 0.9345 0.933.5 0.9545 0.9535 0.955 0.955 0.9505 0.9495 0.9484 0.9474 0.9463 0.945.6 0.9633 0.965 0.966 0.9608 0.9599 0.959 0.958 0.9573 0.9564 0.9554.7 0.9706 0.9699 0.9693 0.9686 0.9678 0.967 0.9664 0.9656 0.9649 0.964.8 0.9767 0.976 0.9756 0.9750 0.9744 0.9738 0.973 0.976 0.979 0.973.9 0.987 0.98 0.9808 0.9803 0.9798 0.9793 0.9788 0.9783 0.9778 0.9773.0 0.9857 0.9854 0.9850 0.9846 0.984 0.9838 0.9834 0.9830 0.986 0.98. 0.9890 0.9887 0.9884 0.988 0.9878 0.9875 0.987 0.9868 0.9864 0.986. 0.996 0.993 0.99 0.9909 0.9906 0.9904 0.990 0.9898 0.9896 0.9893.3 0.9936 0.9934 0.993 0.993 0.999 0.997 0.995 0.99 0.990 0.998.4 0.995 0.995 0.9949 0.9948 0.9946 0.9945 0.9943 0.994 0.9940 0.9938.5 0.9964 0.9963 0.996 0.996 0.9960 0.9959 0.9957 0.9956 0.9955 0.9953.6 0.9974 0.9973 0.997 0.997 0.9970 0.9969 0.9968 0.9967 0.9966 0.9965.7 0.998 0.9980 0.9979 0.9979 0.9978 0.9977 0.9977 0.9976 0.9975 0.9974.8 0.9986 0.9986 0.9985 0.9985 0.9984 0.9984 0.9983 0.9983 0.998 0.998.9 0.9990 0.9990 0.9989 0.9989 0.9989 0.9988 0.9988 0.9987 0.9987 0.9987 3.0 0.9993 0.9993 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.9990 3. 0.9995 0.9995 0.9995 0.9994 0.9994 0.9994 0.9994 0.9994 0.9993 0.9993 3. 0.9997 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9995 0.9995 3.3 0.9998 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 3.4 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 3.5 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 3.6 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.7.0000 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.8.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000 3.9.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000 4.0