Veer Narmad South Gujarat University 2011-2nd Year B.A SB-0142 Statistics higher ( - 2) - Question Paper
SB-0142
[Total Marks : 70
Second Year B. A. Examination March / April - 2011 Statistics (Higher) : Paper - II
Time : Hours] (0_
N Seat No.:
6silq<3i Puunkiufl SnwiA u* qsq <KH=fl. Fillup strictly the details of signs on your answer book.
Name of the Examination :
S. Y. B. A.
Name of the Subject:
Statistics (Higher) : Paper - 2
Student's Signature
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-Subject Code No.: |
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-Section No. (1,2......): Nil |
(0 g U&Vtl WH <HHl.
(y) <H.l$ %|Rei M& UMdl d.
aHL WUH :
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(*l) GcUlkd U&HL [Hh-HSLHL d - S$L.
(0 10 a&faoM &a dUl&di HIHWimI 50 HIM l.
Hl*tt *iKl hkihmI [Hh-hsl %fl*U
(3) 5 5H=ieilMciLlL 20 XX = 980 Ii? = 108 H.L'kt
ilh d. R-hkihmI [Hh-hsl %fl*U *iM.
(>3=0, Z>4 =2.12, =0.58)
(y) (A.S.N.) 5H2<H Hl'SHl Hia
ddi LL ?HlHl :
(m) l*t ciSaiStl S$L :
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Ji |
2 |
J3 | |
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Pi |
2 |
0 |
0 |
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Pl |
1 |
6 |
0 |
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P3 |
0 |
0 |
8 |
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feommn |
A |
uifamH B |
C |
um&i -o |
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I |
5 |
1 |
3 |
34 |
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II |
3 |
3 |
5 |
15 |
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m |
6 |
4 |
4 |
12 |
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21 |
25 |
15 |
61 |
(o) HlHl'Yd H.MHL (&SKI fatMl (0, 0), (0, 1), (-6, 1.7), (4,0) &. Mh Z = 2xj + 2x2 -fl. HtIH &Hd Hiql.
* (?H) GcUlkd UfeHlHi 5HL=ldL dldL MR SlHWiL. M.m ai<Hdl M &d dl M ?1IH ?
M -(IM Hlfecft HVtt X ?Hd R ?HKiH-fl. *441 #t. H.&HL GHHL a*>kl dHRL OfitHl Y'SlWl. >3 = 0, D4 = 2.12 H A A2 =0.58 efi. :
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*l*l<U |
* (?H) X - ?HKiH-fl. VMl ?Hd (3HH>L %LH*M.cCl.
dHRL dR*iLl WZ\i<$L. >3 = 0, Z)4 = 2.12 H A 4=0.58 eft :
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Pii.il : |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
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: |
304 |
288 |
296 |
311 |
300 |
285 |
308 |
296 |
298 |
301 |
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RidR : |
4 |
8 |
12 |
1 |
3 |
2 |
5 |
7 |
6 |
9 |
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HHlfcl WWl.
(<h) 41M *Rdld HLtftd Z = 2x1 + 4x2d HtIH HdWl :
Xj + x2 < 21 2xj + 3 x2 < 48 Xj + 3 x2 < 42 xl3 x2 > 0.
M *[& kk Hl'SHl Hia *R*Rl kktf %LU (ASN) ?Hd *R*Rl |<H dURl (A.T.I.)4l oiSldl M &d iVUHl *llA d ?
(h) =>H Pt*h *ihMl N = 2000, n = 100, C = 2 Hia *R*Rl Mh WtII (A.O.Q.) ?Hd *R*Rl Mh WtII %fl*U
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N= 150, n = 20, C = 1.
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(0 kGd ttHl (3=1141 6%0.Hd H[ci (3) 30-kHL %fl.Hi*it anwiL.
M 5HLHC-1 <H6d<*lci6R &Hl ddH %d<H-(l d 6M ?Hd
(1) As per the instruction no. 1 of page no. 1.
Instructions :
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Di |
d2 |
d3 |
d4 |
um&i -o | |
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Oi |
2 |
3 |
4 |
1 |
50 |
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o2 |
5 |
4 |
0 |
8 |
70 |
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o3 |
1 |
6 |
3 |
2 |
20 |
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30 |
50 |
20 |
40 |
140 |
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(m) iLHL'll ciSaisQ. -ddH &HH HIS S$l | ||||||||||||||||
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(?) <H6d<*lci6R ttHKl <*UH LhL ttH'SA'fl.
(2) Answer all questions.
(3) Graph paper, logarithmic table and statistical tables will be provided on request.
(4) Figures given to the right are marks of the question.
Answer briefly :
14
(1) 'Production process is in control' - Interpret.
(2) On inspecting 10 television sets, 50 defects have been observed as total in all sets. Obtain control limits of chart for number of defects per unit.
(3) From the 20 samples each with 5 obsbervations are
taken, while get X = 980 and i? = 108. Calculate
control limits of R chart. [D3 = 0, Z)4 = 2.12, A2 = 0.58)
What is A.S.N. ? Give its formula for single sampling plan.
(4)
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Person |
Ji |
Work 2 |
J3 |
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Pi |
2 |
0 |
0 |
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P2 |
1 |
6 |
0 |
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P3 |
0 |
0 |
8 |
(6) Solve by North-west corner method to the following transportation problem :
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Origin |
A |
Destination B |
C |
Supply |
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I |
5 |
1 |
3 |
34 |
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n |
3 |
3 |
5 |
15 |
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m |
6 |
4 |
4 |
12 |
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Requirement |
21 |
25 |
15 |
61 |
(7) The points of feasible solution in linear programming problem are (0, 0), (0, 1), (-6, 1.7), (4,0). Obtain the maximum value of objective function Z = 2xj + 2x2.
2 (a) Explain the types of variation occurring in production 7 process. How can the existence of such variations be determined ?
(b) Construct X and R chart from the following data. 7
State your decision regarding state of control.
Take D3 = 0, D4 = 2.12, and A2 = 0.58 :
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Sample No. |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
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X |
98 |
105 |
122 |
90 |
115 |
118 |
108 |
99 |
96 |
104 |
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R |
6 |
8 |
15 |
14 |
4 |
5 |
8 |
9 |
12 |
11 |
(a) Construct X - chart and explain its uses.
(b) For the following data draw mean and range control charts and state your conclusion :
(Z)3 = 0,D4= 2.12, and A2 = 0.58)
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Sample: |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
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Mean: |
304 |
288 |
296 |
311 |
300 |
285 |
308 |
296 |
298 |
301 |
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Range: |
4 |
8 |
12 |
1 |
3 |
2 |
5 |
7 |
6 |
9 |
(a) Explain the construction of p-chart and state its usefulness.
(b) On inspecting 150 articles daily for 20 days, 200 defective articles are obtained. Obtain control limits for p and np charts.
(a) Explain the practical utility of linear programming by giving illustration and state its limitations.
(b) Maximize the objective function Z = 2x] + 4x2 under the
following constrains :
xl + x2 < 21 2x1 + 3 x2 < 48 x1 + 3 x2 < 42 Xj, x2 > 0.
(a) How do you calculate average sample number (A.S.N.) and average total inspection (A.T.I.) in single sampling plan ?
(b) For single sampling plan N = 2000, n = 100, C = 2 draw average outgoing quality (A.O.Q.) curve and find average outgoing quality level (A.O.Q.L.)
(a) State the advantages of sample inspection. Give a brief idea of various acceptance sampling plans.
(b) Draw O.C curve for single sampling plan N= 150, n = 20, C = 1.
5 Answer any four : 14
(1) Give mathematical form of generalised linear programming.
(2) Explain Hungarian method to solve assignment program.
(3) Explain '3cj' control limits.
(4) Solve the following transportation problem by column minima method and find total cost of transportation :
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Origin |
Di |
Destination d2 |
d3 |
d4 |
Supply |
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Oi |
2 |
3 |
4 |
1 |
50 |
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o2 |
5 |
4 |
0 |
8 |
70 |
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03 |
1 |
6 |
3 |
2 |
20 |
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Requirement |
30 |
50 |
20 |
40 |
140 |
(5) Assignment for minimum time :
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Work |
I |
Person II |
m |
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A |
30 |
27 |
30 |
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B |
20 |
28 |
26 |
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C |
24 |
26 |
22 |
(6) Explain general transportation problem.
SB-0142] 7 [ 300 ]
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Attachment: |
| Earning: Approval pending. |
