Pre University Board 2009 STATISTICS in Pdf (KAN & ENG version) - Question Paper

1.    QeFood dZ doO.

2.    wdd drd ,>>,odd 0&,dod ?

*    co    6    eo _o

3.    o>,j<od oddo, d,odrt /d >d (d) n>o 4 <>eA,od ?

_D

4.    y< 4,eo dZw doO.

5.    if dd) Jndodjd n> /d)d) ?

6.    4pe, d}o ,d,o 9 wArort dd d/d (oo dodoSoO.

7.    4d 4rdd dZ doO.

8.    t-d}o ,d,O 0o_J ?

9.    odo woeo Sedo, 3,ed>>:o - A <o >d) 5 wdd,

,ed>o - B o 0oj ?

10.    odo ddddod    odo dd} dS.

II. d>A d/d)ddd drtn Sp :    10 x 2 = 20

11.    odo ddrd, odo drad ,dj,O K,oZ₆doo 1,50,000 wAdod. de ddrd w d&,radS old edoS    ,oZ, 6,000 wAdoSd.

co    eo    co    6    -c

jnjdd ds, dddo dodoaoO.

1$    ct

12.    S P ₀ q ₁ = 250 doSo S p ₁ q ₁ = 400 wdd, idd ioddo dodoaoO.

13.    n3 d ijodd djZ doO.

14.    y< ,e ed}do 0ddo d<dertrt>o .

V    CO    ct

15.    odo a,dd Sd}do ,dj,O 4 doS 5 wAdoS d.

o3    0    _o

e$ddo doe ieddra aea doSo ado_& ieddrad, yjdra da.

16.    odo ud/₆ >Sd}do, p ₁ doSo p₂ n> drt> dod ?

17.    d/d 3 dod od ,dojood 25    odo d/dd do doo wO SrtdooAd. dodo ,dj,Odo adoS deddb, dodoaoO.

18.    ode d doSo 0dde dd dedrt> djZ doO.

19.    odo -ed*" dd ISosspdd) 7 wAdjrt, dd ,dj,O doSo doo dodoaoO.

20.     d> A L.P.P. (,d > deedo d,dop ,do,₆) dob, rtdoa :

aod ndj,

x + 2y < 9 x < 3

do So

_D

x > 0, y > 0 wAdJ n, Z = 3x + 5y rtOdrt$&.

CO ⁷    ct    

odo de> x = - 2 doSo y = 4 wdd, dodo d&j L.P.P. rt d Od djrtod)de ? ado_& Sdd yjdrado $.

21. X> A A db e-w d/Xrt B db e-w d/Xdbb dbO :

22.    edoX rtbra adborad d/d)ddd 0dd dertrt>b $&.

- C

iii. x> Ad)n> d/d)ddd 000 d_;4_tnn o :    8 x 5 = 40

oydr dodS,, dSod dido idaiO JXd) 5 S.na,o.AoJ XSdo ddbe 0odo dOeS.

30.    odo iad/₆ dd <doo 81 wAd. dd 21 d,ort> (doo 100 wAd. 1% oyadr dodS, do<do <doo idoido ood $ddaAd <doe 0odo dOeS,.

ct    oOk

5% o"3\wr dDjd,, dsd) dXodJoddSD, Xsdo d/dod)de 0odD sd)

$d>D,Dd ?

32. d_;DJ_cz JJdSb, deA&, X>AS edDS s.

33. odD DoJ;d <dd d&. 40,000 wAd. ed ed ddrrt>, dd dDdDX_;D d J ad r } d rt>SD. X>n XdosAd :

ZJ    -e    1$    ot

34.    odo oea S/oss doo, dedoX bdsSd) p¹ = 001 wAdoSod.    aooSxd) 100 nsS,d)> dodo do><d doe doondd, np-dezsSxd ( np-chart ) abOSra bn>b_CR Xodb&Soo.

- D

iv. x> Ad)rt>, /d)dsdd 0do dnn Son :    2 x 10 = 20

35.     X>A dsoaod A doSo B rtdrt> Xs dodra dd doSo aoSXS dodra

_o    _o    _o    >

ddn>o_J Xodb&Soo :

ot

36. X>A dSo <d ,s₆oXdbR XodbSoo. d ,spXd) Xj dSo ,doo ddsdSr doeX\ doSo ddSr ddsdSr

d o X@ add d}(do on) doo 5% oiSr dod, add d } oo , doo&,de 0odo dOea.

- E

V. X>A /d)de 0rfo dn O :    2x5=10

39.    odo srad/₆ d}oY Q ₁ =40 do Q ₃ =60 wAdod. d}o , di, O, odrd do a <rt>o dodasoO.

40.    odo ira,dd 400 ,< dvOiAd. w 400 doo_tXn> 220 ,<

6 <=i    o    o    c-3

<do dddoioo. 5% 055\jr dd, >ra₆d d)dadiAd 00 di/dX, id) dSod ?

41. ddbd dbbo Xjd rtbrart>o dodiAdbe 0odb dOeS\,<b 100 doa X,d, d dd 200 dboa X,d, d de daZdd,

eUk qj    _o    eUk qj    ct

d/dcibd. dazi dio X>Aod :

1% <yi\wdr dbjd, -ed¹ dOeXdd >.

42. od d rX, 10,000 dd n> esX d. dA dodd dd d. 200

v    >    Li

dd adrd}i dd) d, ddrt d, ddrX@ d&. 10 dA doXddd dX.radci dd d dd dd n> Xddrt dyi . dinidd

oOk    CO    0    _0    _0    CO

i)    ddd ,dS rrad,

ii)    db.d do esXn> d ,d<d

) _D

iii)    sbdb eSXrt> ,oZ₆

iv)    Xa dirX ,di,O ,ort,d}i dE

   j/    i$

d)rt>d, XodosbO.

Note : i) Statistical tables will be supplied on request.

ii)    Scientific calculators may be used.

iii)    All working steps should be clearly shown.

SECTION - A

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.

SECTION - B

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 :

22. State any two uses of Statistical Quality Control.

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

24.    Define Index Number. State any three uses of index numbers.

25.    From the following data, compute Consumer Price Index Number by

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.

Can we conclude at 5% level of significance that Dhyana reduces Blood pressure ?

32. Solve the following game using the principle of dominance :

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.

SECTION - D

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 :

Estimate the production in 2009.

38. Seven coins are tossed 128 times and the following distribution is obtained :

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 :

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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