Pre University Board 2009 Statistics ( kannada & english sersion) - Question Paper
STATISTICS 2009 in Pdf is in attachments check tat.
[ Total No. of Printed Pages : 15
Code No. 31
Total No. of Questions : 42 ]
( Kannada and English Versions )
Time : 3 Hours 15 Minutes ] [ Max. Marks : 100
( Kannada Version )
: i) sraoX XejXrt>R Xe$>rt X>rio4)o-
ii) 4,q>>X n raXe Xd (eA,oo.
<=i
iii) 5>of 0| 0n>R rOjjiA eD,X@Q.
- A
I. X>A 0> 44rt>o 0 : 10 X 1 = 10
7 l <=i >
1. aeFood do0.
2. wd f ,>.oX 0 0&,dod ?
* co 6 eo _o
3. >,j<d 0 ,6oX2r dorort >d (X) rt>R <>eA,o>d ?
_D
4. 5> ,e(o doO.
5. 1f dj JrtdoXo drt>o ?
6. Pe,> d}(o ,d>,0 9 wArort - /X <or Xoo&SoO.
7. fX i6Z6 doO.
8. t-d}o ,di,0 0Oj ?
9. oo w<oeo ,edoY 3,era>>o -A o >4 5 wd,
S,era>>o - B o > 0oj ?
10. oo >jXYdo4 oo >d} XS.
II. d>A d/d)d,dd 0_O drtn O : 10 x 2 = 20
11. odo ddrd odo d&rad ,d>,O K,oZ6doo 1,50,000 wAdod. de ddrdS w d&.radS oi>d edo ,oZ. 6,000 wAdod.
co eo co 6 ->
>n>dd d> & dddo dodoaoO.
12. 2 P 0 q 1 = 250 doo 2 p 1 q 1 = 400 wdd, jdd d oddo, dodoaoO.
13. n>d d ,>odd dZ doO.
14. y>< ,e ed}<do 0ddo ddertrto
V CO ct
15. odo a,dd d}do ,d>,O 4 doo 5 wAdo d.
o3 _o _o
deddo doe eddra aea doo ado& Jeddrad y>dra da.
16. odo ,>d/6 d}oY p 1 doo P2 n> ddrt> 0jod ?
17. d/d 3 dod od ,doood 25 n>d)> odo d/dd do doo wo Jrtdoo>Ad. dodo ,d>,Odo ado dedd dodoaoO.
18. ode d doo* 0dde dd dedrt> dZ doO.
19. odo -ed*" dd oodd 7 wAd>rt, dd ,d>,O doo dooR dodoaoO.
20. d> A L.P.P. (,d > deedo ddop ,do,6) do rtdoa :
aod rtd,
x + 2y < 9 x < 3
doo
_D
x > 0, y > 0 wAd> rt, Z = 3x + 5y rtOdrt$.
CO 7 ct o
odo de> x = - 2 doo y = 4 wdd, dodo L.P.P. n
d Od d>rtod)de ? ado& dd@ y>drado
21. X>A A o e-w /Xrt B o e-w /Xo doO :
|
B | ||||||||||||||||
|
22. oX rtora ><oora /)d 0do ertrt>o
- C
III. X>n)rt>Y /)d 0o&o O : x 5 = 40
Xoo&SoO :
|
23. X>A >oQo oX d od ,on, <oX drt>o &)e>x3 ( z!rri>Q ) |
ori,d a,oZ6 |
,oZ |
c~ ASFR |
|
15 - 19 |
10,000 |
500 |
10 |
|
20 - 24 |
15,000 |
900 |
100 |
|
25 - 29 |
14,000 |
1,400 |
120 |
|
30 - 34 |
13,000 |
800 |
90 |
|
35 - 39 |
9,000 |
400 |
50 |
|
40 - 44 |
6,000 |
150 |
20 |
|
45 - 49 |
3,000 |
50 |
10 |
24. ,6oX doO. oXd /)d odo ertrt>o
25. X>AS dJoX, n>,dX d .oXdSo Xd&do d Jd,} dSaod
_o 6 y 6 ot *
XodoSDO :
| ||||||||||||||||
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26. X> AS y< ,ert Jot&fX <S3 ,o,Ort> dDX dd ddrt>0 |
|
XodoSDO : | ||||||||||||||||||
| ||||||||||||||||||
|
27. odD SrtDodD odD ,eJdrt Jrtcod ,oddaeidDJ 1 wAdoJd. sod, * 2 - &snodbrt>So od ,eJDdrt no d/S d>Ad. ,?JDddSD d,o,rt$,co <=i <=i oi dDcb &snodbrt>D JrtSdd ,3Xd. |
i) ,Jod dd dond
ii) <d/d)de SrtDodo ,eJbdDo Jrtde cbd ,oddaeDJrt>SD XodDSDO.
ot
28. odD ddd adrdS odD aDddS ,-3,o 3 d>dd Xdrt>So
co <=i
eXOj&J. odD aarj aDddS, d>o
i) <d/>d)de Xd n>D eXO,d
ii) 0d d S.oJ d e Xdrt>SD fyeXOj&d
6 ti ot cd
,oddaeDJrt>SD XodSDO.
ot
29. odD <d/d,X SdS<dD0dDd 100 d,rt>SdDd dS,,<dD JXd
ZJ ey cn zJ cn <yJ
,d,O<dDD 497 3.TO0. dJ d/X (dDD 02 3.TO0. wAdoJ d. 5%
Zs o J/ _o
osdr ddS,, driSd dS;,<dD ,d>,o JXd) 5 a.no.AoJ XsdD d<de 0odD dOeS.
30. od ,d/6 dd <S<dD 81 wAd. dd 21 d,Drt> <S(dD 100 wAd. 1% osdr ddS, SdDSd S<dD ,d<d SDod SdAd <de 0odD dOeS,.
ot ed
31. X>n 5 dd >6 /4d co
|
oSd . _D | ||||||||||||||||||
|
5% OffSF Oj0y, XoSo0r XSD 0OD
32. 4$ 4efln, X>n S/ed Sn.
|
jt&d>3 - B | ||||||||||||||||||||||||
|
33. o <oS, $ d. 40,000 wArf. $ed $ed rrt>, -dX;( $ f } d rt>. X>n XosArf :
ZJ -e t3 ot
| |||||||||||||||||||||
|
OOS, ,XoS aron. |
34. oo oea deoo p 1 = 0-01 wAdorf. 4$o ><oo,ra4 100 4o0 4o><o 4oe 4od, np-dez>te ( np-chart ) ><oora ort>0 dookSoO.
- D
IV. X>A)rt>Y 0-3 4,4 O : 2 X 10 = 20
35. d>A >o4Qo A 4oo B rtdrt> d 4odra d 4oo a<od 4odra
_o _o t3 _0 >
drt>0 do4oSoO :
ct
|
( ) |
Sfitf- A |
n- - b |
a,oZ6 | ||
|
a,oZ6 |
a,oZ6 | ||||
|
0 - 20 |
5,000 |
100 |
7,000 |
105 |
1,000 |
|
20 - 50 |
14,000 |
392 |
15,000 |
465 |
5,000 |
|
50 - 70 |
20,000 |
300 |
25,000 |
500 |
3,000 |
|
70 4d0 _D 4oe<j0j |
1,000 |
200 |
3,000 |
390 |
1,000 |
36. d>A do <>4d ,6odOR do4oSoO. <>4d odj dj 3oo4d@ ,400 4d"34F 4Oed\ 400 44F 4d"34F
|
4 Oed.rt >o 4S, 0oo eO : oOk c y _D _0 | |||||||||||||||||||||||||
| |||||||||||||||||||||||||
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37. y = a + bx + cx 2 d<db db bb, rtr >Qo ,ode : | ||||||||||||||||
| ||||||||||||||||
|
2009 e fS bb oro&. CO <yJ 0 ct |
|
38. a>b sra.rtb, 128 ,< b.cafirf bb X>n drabb, d<bc>Arf: > t O o ct | ||||||||||||||||||
|
o2 X@ Q >d}bb zb bbo 5% <y\wr d } (bb ><b , bO,e 0ob Oea.
- E
V. X>A /)de 0rfo O : 2x5=10
39. ob sra/6 d}bY 9 1 =40 bb Q 3 =60 wftcbrf. d}(b , o>, O, brd bbo a< <rt>b XobSbO.
40. Ob ra,b, 400 ,< W 400 bbvxn> 220 ,<
6 ct o o c-3
Cbb, dbcbb. 5% <y\wr bj0Y 00
$3/bX@ drf ?
41. oOo ,X\d rtorart>o oaAoe 0oo Oeaoo
|
X.d, do <*A cp |
25 |
75 |
100 |
|
X,d, do oOk Cp |
50 |
150 |
200 |
|
Dj |
75 |
225 |
300 |
1% <y\wr ojS, -ed1 OeXjo
/oaod. za Sao X>Aorf :
42. oo fX, 10,000 ,o n> esX doA do,o d&. 200
v > Li
oOo >f}3 ,0on rX@ d&. 10 doA doXodo
X,raoa rto od n> XdJrt . anad
oOk cn o _o _o cn
i) d.wD ,da na
ii) o esXrt> o ,oo
) _D
iii) 3o63eo eSXrt> ,oZ6
iv) X ot&fX ,da,O ,ortj}a
j/ i$
rt>0 XooSoO.
Note : i) Statistical tables will be supplied on request.
ii) Scientific calculators may be used.
iii) All working steps should be clearly shown.
I. Answer the following questions : 10 x 1 = 10
1. Define Longevity.
2. What is the value of an index number during the base year ?
3. Which weights are used in the construction of Laspeyres price index number ?
4. Define Time Series.
5. What are the values that a Bernoulli variate can take ?
6. If mean of Poisson Distribution is 9, then find its Standard Deviation.
7. Define Statistic.
8. What is the meaning of t-distribution ?
9. In a rectangular game, the gain of player-A is 5. Then what is the gain of other player-B ?
10. Give an example for defect in a product.
II. Answer any ten of the following questions : 10 x 2 = 20
11. In a year, the average population of a town was 1,50,000. The number of live births occurred in that year in the town was 6,000. Find the Crude Birth Rate.
12. If 2 P 0 q 1 = 250 and 2 P 1 q 1 = 400, compute suitable price index number.
13. Define Consumer Price Index Number.
14. State two uses of analysis of Time Series.
15. The mean and variance of a Binomial distribution are 4 and 5 respectively. Comment on this statement and give reason to your comment.
16. What are the values of p 1 and p 2 in a Normal Distribution ?
17. A random sample of size 25 is drawn from a population whose standard deviation is 3. Find the standard error of the Sample Mean.
18. Define Type-I and Type-II errors.
19. The degrees of freedom of a Chi-square variate is 7. Find its mean and variance.
20. Consider the following L.P.P. :
Maximize Z = 3x + 5y,
Subject to x + 2y < 9 x < 3 and x > 0, y > 0. suppose x = - 2 and y = 4.
Is it a solution to the given L.P.P. ? Give reason to your answer.
21. For the following pay-off matrix of A, write down the pay-off matrix of B :
|
B | ||||||||||||||||
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22. State any two uses of Statistical Quality Control.
11 Code No. 31 SECTION - C
III. Answer any eight of the following questions : 8 x 5 = 40
23. From the following data, compute General Fertility Rate and Total
|
Fertility Rate : | ||||||||||||||||||||||||||||||||
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24. Define Index Number. State any three uses of index numbers.
25. From the following data, compute Consumer Price Index Number by
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Family Budget Method : | ||||||||||||||||
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26. For the following time series obtain the trend values by finding |
|
3-yearly moving averages. | ||||||||||||||||||
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27. The probability that a bomb hits the bridge is 1 . Four bombs are |
aimed at the bridge. Three bomb-hits are enough to destroy the bridge. Find the probability that
i) the bridge is destroyed,
ii) none of the bombs hit the bridge.
28. On an average a telephone operator receives 3-telephone calls per minute. Find the probability that in a particular minute she
i) does not receive any call
ii) receives more than two calls.
29. A random sample of 100 tins of Vanaspati has a mean weight 4-97 kg and standard deviation 0-2 kg. Test at 5% level of significance that the tins, on an average, have less than 5 kg Vanaspati.
30. A normal variate has variance 81. Twenty-one random observations of the variate have variance 100. Test at 1% level of significance whether the sample variance differs significantly from the population variance.
|
31. The following data represents the Blood pressure of 5 persons before and after performing Dhyana : | ||||||||||||||||||
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Can we conclude at 5% level of significance that Dhyana reduces Blood pressure ?
32. Solve the following game using the principle of dominance :
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Player A |
|
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33. The cost of a machine is Rs. 40,000. Its resale value and maintenance cost at different ages are given below : | |||||||||||||||||||||
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Determine the optimal age of replacement. |
34. In a fish-net manufacturing process, the proportion defective is p 1
= 0-01. If process control is based on samples of size 100 each, find the control limits for np-chart.
IV. Answer any two of the following questions : 2 x 10 = 20
35. From the following data, calculate Crude Death Rates and Standardised Death Rates of two cities A and B :
|
Age ( Years ) |
City - A |
City - B |
Standard Population | ||
|
Population |
Deaths |
Population |
Deaths | ||
|
0 - 20 |
5,000 |
100 |
7,000 |
105 |
1,000 |
|
20 - 50 |
14,000 |
392 |
15,000 |
465 |
5,000 |
|
50 - 70 |
20,000 |
300 |
25,000 |
500 |
3,000 |
|
70 & above |
1,000 |
200 |
3,000 |
390 |
1,000 |
|
36. For the following data, compute Fishers Price Index Number. Show that Fishers index number satisfies Time Reversal Test and Factor Reversal Test for the given data : | ||||||||||||||||||||||||
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37. For the following time series fit a parabolic trend of the type y = a + bx + cx 2 by the method of least squares. | ||||||||||||||||
|
Estimate the production in 2009.
38. Seven coins are tossed 128 times and the following distribution is obtained :
|
Number of Heads( X ) |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
|
Number of Tosses ( f ) |
7 |
7 |
21 |
30 |
26 |
20 |
14 |
3 |
Fit a Binomial Distribution to the data and test for goodness of fit at 5% level of significance.
39. In a Normal Distribution Q 1 = 40 and Q 3 = 60. Then find Mean, Quartile Deviation and Standard Deviation of the distribution.
40. A coin is tossed 400 times. Among these 400 tosses, head appears 220 times. Can we conclude at 5% level of significance that the coin is unbiased ?
41. In order to test whether attributes Smoking and Literacy are independent, a survey was conducted on 100 literates and 200 illiterates. The result of the survey is as follows :
|
Smokers |
Non-Smokers |
Total | |
|
Literates |
25 |
75 |
100 |
|
Illiterates |
50 |
150 |
200 |
|
Total |
75 |
225 |
300 |
Apply Chi-square test at 1% level of significance.
42. There is a demand for 10,000 items per year. The replenishment cost is Rs. 200 and the maintenance cost is Rs. 10 per item per year. Replenishment is instantaneous and shortages are not allowed. Find
i) the optimal lot size
ii) the optimum time between orders
iii) the optimum number of orders
iv) the minimum annual average inventory cost.
[ Turn over
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Attachment: |
| Earning: Approval pending. |
