DU SOL Question Paper 2018 B.Com (Hons.) Business Statistics

[This question paper contains 20 printed pages.]

s89 Your Roll No. .............

B.Com. (Hons.)/I G

Paper Code : A-105

PapeT IV - BUSINESS STATISTICS
Time : 3 Hours Maximum Marl<s : 55
Tltlzt : 3 qut
qvfu : SS

(lTrite your Roll No. ort the top immediately
on receiPt of this question PaPer.)

(tv vw-w I rqile # 6c( frv w
fruffri Ftq w ss4r 3ryfict6 fufuvr)

Note :- The maximum marks printed on the question paper are
applicable for the students of the regular colleges
(Cat. A). These marks will, however, be scaled up
proportionotely in respect of the students of SOL at the
time of posting of awards for compilation of result-

wFr-w w altud Ytfd Ouft A) i t{ar qf,ffi + frufuT
+ fts aSrqlw * r dqfr t ntq soL * ffi + #r
+' 3-d-A qfum * eqaq + frs frgffi aidfuiq i qqq w,

;4+ aryqfda 6c +; a$rq ahT t
Note :- Answers may be written either in English or in Hindi;
but the same medium should be used throughout the
PaPer' P.T.o.

s89 J

Eq'vft:- Eq s-ff- w 6r rtr ,?,+d' qr ffi Enfr (q wqr * ffrV;
tftt. trrff wrd' mr qF-wr Yq f #dI qftv r

Attempt all questions'
Use of simple calculator is allowed.

irsff rfl +?rGgr
qF{RqT *tq-fu qT 3r+Fr qrq *r

1. (a) The tbllowing table gives the distribution of weekly
income of 320 families:

Weekly Income (Rs.) No. of Families

6,000 - 8,000 40

8,000 - 10,000 80

10,000 - 12,000 100

12,000 - 16,000 64

aa
16,000 - 20,000

20,000 - 24,0a0 4

Using appropriate percentiles, answer the following:

(i) What are the limits within which incomes of the
middle 50 percent of the families lie?

589 3

(ii) lt is decided that 80 percent of the families should
pay income tax' What is the minimum taxable
income'l

(iii) What is the minimum income of the richest 30
percent of the families'?
of 100 items
(b) The mean and standard deviation of a series
While
were found to be 60 and 10 respectively'
as 5 and 45
calculating, two items were wrongly taken
variance'
instead of 30 and 20' Calculate corrected
standard deviation and coefficient
of variation' (6+5)

OR

(a) The followrng data are given fcr two
companies'

Clombining data for groups of male and female
emploYees, find out

ComPanY A ComPanY B

Males Females
Productivity per employee Males Females

Mean 30 20 27 32

Variance83125
No. of emPloYees 4A 10 20 30

(i) Which company has a higher productivity per
emPloYee?

P.T.O.

589 4

(ii) Which company has more consistent productivity?
(b) (i) The sum of 20 observations is 300 and the sum of
their squares is 5000, find the coefficient of
variation and coefficient of skewness, given further
that median : 15.

(ii) For a moderately asymmetrical distribution, the
mode exceeds mean by 15. Estimate the value of
median if the mean is known to be 80. (6+5)

I (6) ffiRe-d drkfir 320 cfrsr* sft {r<rtrs. arq 6T frttq v{rq
q-cft *:

lsrqG6'erq (c.) cffii 6t *{sr
6,000 - 8,000 40

.l0,000
8,000 - 80

Io,00o - 12,000 100

12 ,000 - 16,000 64

16,000 - 20,000 32

20,000 - 24,OOO 4

3cgffi {tdilIFF (cif'cr{d) q.r vfrrr q-t*, fiqfrke -FT crr
fifrq:

5
589
(i) q?q 50 uRsrd qffi d 3{q fr-{fr{rst + 3ff( 3{rfr
}?
b:

qffi d snq-+t 6T Trrdn 6-fiI
(ii) FftIIRd t fr eo vRrrf,
qrGqr {d-{-dq a.r *rq 3nq
4r ?i
cffi fr q:rcq snq an ??
(iii) {qtRffi {"{a 30 cR{rd
qna ett qrro R-{d{ d a-qu'
60 1'dl
(ta) roo eqfr m *ft
*
q-'A + *rra' a q<3] d so
sfu zo
slTl rrqial
10 qrql wtr qt RqI {qr
qt q{f, w t s :fu as * w i rraor
* anq
fr-rn'r rTqr6 6r
qRq_dq
qrr qfrEra wRUt' qn-o tr-qa;r \r{
dRqr
$?raT
qtrdr
+ ftq ftqRfr( di6t Rq rrq er $q sq
(q) n 6qFd ;rgm a-r' gra frRqt
q6,ffii * s{a + Rq ;n*i d
affiA affiB
g€s qtrdr
qR-dr
qft 6ffi 3f,rr6-dT sq
20 21
30
qTt4

J l2 )
8
q{tgr
20 30
10
fr {@r 40

P.T.o.

589 6

(i) frq q.qfi d efd q-ffi ireneq-ar ,r.q *r
(ii) fr'€ qtTft d 'rsreq-m s,rft-fi Svrrd (consistent) i?
(re) (i) zo ierofr qr *Tr s00 vcr t-ag u6 q.r *rr sooo *, qR
iq-+t qTDqfril = t5 * + R-d{ur {uns- \r{ aqq r-run-€
(coefficient of skewnessl ara dftVr

(ii) qtqq imqfr'd R-fiqT + frq qnq fr ge+ fr Ergdfi q.r
qFr ts erEro ir qh qna tnT rrcr eo * * qrEq-*-r +
qr;r tnl 3{Frtr{ dfrqr

2. (a) The sales made by a firm over last few years are given
below:

Year: 2009 20ra 20t1 2012 2013 2{}t4 20t5

Sales (rn lakhs of Rs): 80 90 92 83 94 99 9l
(i) Fit a straight line trend to tl-ie data using the method
of least sqllares, and obtain the trend equation
taking 2009 as the origin.
(ii) What is the average annual change in the sales?
(iii) Estimate sales for rhe year 2017 using rhe trend
equatlon.
(b) In a working class budget enquiry in Towns A and B,
it was found in a certain year that an average workirrg
class family's expenditure on fbod and other items was
as follou's:

589 7

Town A Town B

64% 50%
Food

Other Items 36% s0%

number stood at
The rvorking class cost of living index
279 for Town A and 265 for Town
B' It is known that
by working
the rise in prices of all articles consumed
classes was the sanre for A and
B' Find the index
numbers for (a) food and (b) other
items' (6+5)

OR

4 percent in 2006'
(a) An index is at 100 in 2005' It rises
falls 6 percent in 200'1 ' falls 8 percent
in 2008' rises l0
percent in 2009 and remains same
in 2010' Further' in
2011, it rises by 7 percent and
in 2012 it falls by 3
form of link reiattves
percent' Put this information in the
into price relatives
and then convert these link relatives
taking 2005 : 100'
garments
(b) The seasonal rndices of the sale of ready-made
given below:
of a particular type in a certain store are
I li iil IV
Quarter:
Seasonal Index: 84 92 91 130

(i) if the sales in the first quarter of a year be
Rs

28.600, determine how much worth
of garments of
each type should be kept in stock
by the store to
quarters'
meet the demand in each of the remaining
P.T.O.

589 8

(ii) If the total sales during 2017 are expected to be
Rs 200,000, prepare quarterly sales budget using
the siven seasonal indices. (6+5)

(o.) ffi Ed sd + +{T.n{ ara d vr {fr d'fr ffift+o i:
ed 2009 2010 2011 2012 2013 2014 2015
'
fr-fr (arce tc+ +) : so eo s2 83 s4 ss s2

(i) fr€ F+q{ fiEr o.r Bq+rr o-r+ dTH,' + frq fr?ft t€r
v-.eR lstraight line trend) fra-d dfrq, V€r 200e -i 1w

R + s''T + rq+rr o-c+ ygfr {$-swr srw dfrqr
(ii) Rftzit n *€-d qrffi*. qffi.r wr l?

(iii) y-gfr Tfi-*-tur *.1 3c+{r o-{+ Ed 2017 + frq trFq} 6T
3{rs-cffi dfrqr

(q) srfi A \rd{ 116{ g i o.m+-rfr crf qqc Tfdrir * *ir+ 1'*.
fiF-dd e{ + a6 qffi T{tt fr qtffi eilt rq q* .n *s-d
q.mfirfr qlf cRqR iFI Et€T ffifr{d r+R t qt:

sr6t A sr6{ B

qtq-d 64% s0%

3rq sEq 36% 50%

9
589
qtt m *T * e' * Re zzs
frffi as-6 trqr d
6Tq6rs
* ard e m qrq-orfr cd ant
{q {rrt e * Rq
;; ?r
* qs i o u * 1I:
iq$., m q-{ *.n
"re.t eq$ * fr{q wmT-{
(b) ;
T {{qrq
6qa ailr (.) 't{-nq-*,;
(lndex nunibers)
an dffigt
3r9jrefi

{6{r
i 1oo qt *r qa zooo il a cfrrf,
(q) qa' qs61-+. zoos qfdr ?' zooa fr a cfrrsrd FR
6rdl

l, zoor fr u ;* fiR t qq. sqr< rdat
qd zolo
{d . rfrt ?
*, zoos q to onu* (6 € qrat t etu
ir srs *-*:;;t
i' qa
' T*
*r E{ srd+rt A '$'<efrrd
aolz I t o; -* * srm qr€ 2005 100 ae €q Ed
** =
3{tRffi * t'q i 3{k 3s-+

d 1ugu'( fr tqrdRn frRqt
3{qfe-dr
';<eftf, + ffi
(ta) s6 ftfrqn d d ry * * tfits q€+ m Grfi
Rq rK E:
{qola. fra
q-6-& st ffi +?ft
Frqrfi:
8 a e2 94 130

druft W6r*'
e fr ze'600 d'
fr RFrqi d fr
qR qq m q6fi frlqrfi qitr d
re-+. ftHffi i
(i)
dt tq
FftfF( frRe f
srn
Y-on *
qa fr
tr-d+ {€ + e-e6
* ; + Rq qrtrql
qrar d-o I (ft Grft p.T.o.

s89 10

(ii) ,rtr 2cr7 + dt?rtr E-"r zoo,coo a Efr frfird irtfkd *-
+ ftq rq qM q-qq.m q;r:wiFi qr* ffi ffi qwe
frffi,:; qifrqr

J. r3) Civcn tlre foilo,uviltg daia:

rt = 12. IX:12A,2,{: i.}9:. f\"" 432. IY2 = 18,252,
arrri IYI' : 4.992

L l.leulutc tltc' li,l lu\\ inu:

(i) The two regrcssioi-, coefficients
tri) l-he t\\'o !-f.rres.i{';l .''.1 .taltGns
(iii) Tlit c.,ef i'icieti rli correlation between X and Y
(b) (i) Tire cc-ei'iici;:rt of correlation between two
ve;-icbies X end Y is 0.4 and their covariance is 12.
if'vaiiance ci X series is 9, determine the second
momerit about mean cf Y seri es.

tiit For a nresokurtrc distribution, coefficient of
i'alia,,ioir - 4{}!,,t anri arithmetic mean = 40. Find
the iairic oi its {'ourih central moment. (6+5)

OR

iaj A sample oi cigirt employees is taken from the
rlroduction cl€paitment of a light engineering tactory.
'fhe riata iitat lo!low relate to the number of weeks

589 11

experience in the wiring of components, and the number
ofcomponerrtswhichwererejectedasunsatisfactorylast
week:

EmploYee A B C D E F GH
Weeks of exPerience 4 5 7 9 l0 11 12 14

Numberof rejects 21 22 15 18 14 14 11 l3

(i)Calculatetheco.efficientofcorrelationforthese
data and interPret its value'

(ii) Find the least squares regression equation ofrejects
on exPerience.

(iii) Predict the number of rejects you would expect from
an employee with trvo weeks of experience'

(b) The first four moments about origin of a distribution
are known to be 8, 100, i100 and 12,976'

(i) Calculate co-efficient of variation of the
distribution.

(ii) Comment on its kurtosis using beta coefficient'
(6+s)

3. (q) Rq Tf} Btd
n:12,2X:120, EP = 1,392,2Y= 432,212: L8,252,
and EXY - 4,992
P.T.O.

589 12

n frs{Rfrdd q.r qfrs-tr{ dfrg:
rit et qFr{iffi rrunfr

(ii) A sfu{HT {fiF,{ur

(iii) X 3*r v + fiq e?rffiu-1vrrfr

(€) (i) d qtl- x Biit \'+ fiq rrrcqu-riunf, 04 * 3ik 3{nI
TgeeREl tz *r qii x Tls-{r q"I llrnq s i, d Y Ti{flr

d erux * qeu fr FSq' arEi o,r FHt{tT dfrqr
(li) qtnstA ftdiuT t frq tr-utur rurl-fr = 40% gs €qa-t
qltq = 401 Eq-+ -.ft+ *fm '3r'S {tburrh central
nro:i:eut) -frT qI{" gre *fuqr

we;felT

(q.) arrc :'dtfuqfrn +nts* *' c-rirrc i-niTr{ t wd q'm- 6T

efrqifr ftqr ur-+r dr {flS qT{ crq €J+ sTA 3{r+= :rtr* m
erqfrT q-r+ iffiu1 eT-{ifi €'aFi qt q'teir, qs FritA r-$-}
*
orrsq-d-iq. *+ + qr<q fr-rFT kq rq .3{-qq-d- +1 rnqr t
wrfire *:

e;Sqrfr ABCDL,FG}I

sqv<*uwra 4 5 7 e lo 11 12 t4

FR€ fr'q rrq ii-qr* fr €tqt 21 22 ts tB 14 14 tt t3

589 13

(i) F{ 3{d + frq {6€d?r {tnfi q.r qRq-f,{ mRq 3i{
w+d qn fr dn-{dlt +1Rqt

(ii) $T{s cr< A+ qr frr< frq rlq sql-i fr rirqr qt
{d-dq qrt sfurq-{ {$-5-iur an dfrgt

(iii) a 'tr<tl-d inT s3r-q vrq q-ffi t 3rEfkd w t fitw
fuq qr+ erA 3 +q=* a'i ritqr o-r gci--{tm ern{gl

(e) Rrrq fr s€R + €du t an 9qq qR ataoi e, 100,
'1100

*t rz,qzo it
(i) tr'+tur + fr-diur 1vno o.r cfr*-f,{ dRqt

(ii) Etcr {o1,6 e;I 3q*rT 6i-* Eq-dr -[6.-EilI q{ fr'qfr frRqt

4, (a) A drug rnanufacturer believes that there is a 0'98 chanr-e
that the Drug Controller (DC) will approve a new drug
the company plans to distribute if the results of current
testing show that the drug causes no side effects' The
manufacturer further believes that there is a 0'40
probability that the DC will approve the drug if the test
team of
shows that the drug does cause side effects' The
physicians working for the drug manufacturer believes
there is a 0.15 chance that tests will show that the drug
does cause side effects'

P,T.O.

589 t4

(i) What is the probability that the drug will be
approved by the DC?

(ii) If the drug is approved by the DC, what is the
probability that it causes side effects?

(iii) What is the probability that the drug causes no side
effects. given that it was approved by the DC?

(b) A manufacturer who produces medicine bottles finds that
0.19'o of the bottles are defective. The bottles are packed
in boxes containing 500 bottles. The manufacturer
guarantees that not more than two bottles in a box will
be defective. Using Poisson distribution, obtain

(i) The probability that a box selected at random is
free from defective bottles.

(ii) The probability that the manufacturer will not
receive any complaint.

(iii) The probability that a box rvill fail to meet the
guaranteed quality.

(Given: e-02s : 0.7788; e-0'5 : 0.6065; e-0'r : 0.9084)
(6+5)
OR

(a) If a machine is correctly setup, it u'ill produce 90 percent
acceptable items. If it is incorrectly setup, it will produce
40 percent acceptable items. Past experience shows that
80 percent of the setups are correctly done.

589 15

(i) li after a certaiu setup' out of the t'irst two
items
and second
produced. first is fc''und to be acceptable
that machine
unacceptable, what is the probability
is correctlY setuP?

(ii) If the machine produced first nro items
as

tlrat the machine
acceptable, what is the probabilitli
is correctlY set-uP?
(6+5)
(b) Discttss the propertics of normal distribution'

q-fqFT cteTor qftunm +
(o.) v+ siqGl frFrqif,I e;{ freqm e fu
g*-{d) qxrfq q dI+ qt q-qft
eilsFl Era'atg q{d vqrq (eTgs
sirqF': qr fr{ilT
ftf{ q.i+ * 4sa futRa e' 3+ gftsEr
ERT

ffi{6 (DC) anr s1*fra fuq sr+ fr o'sa erTrdaT *r rq-t
ilfrfi-fi lbFr4kT d qa q fr-rs|{ A fr.'
qfr qfre{or E$lfdT e
g' *
fr Ee 3mt * *€ cT$-d eqrq ({E-s eh+e) srE{:
fi 3ilshi Frar+' (DC) gln gMr 6r a-"dqa 4{+ S
0 40 slE-dffir
g' '3ffi"1 frFFTt-iT + frq qd q.* qrfr ftrM
m &q qr R'ssT-{ g fr cM.. i iftqFl Eitr sq-fr:
qv-d et{rq

(ergE g+en) Eqiq -3T+ dt s'15 q.{rfir ir

(i) slNl FP-c-s- (Dc) a{T orMr
qr 3TTfr-dq mtt *t
gri{s-dr @T 6:

(ii) qR ffiI d 6M'r ffi{-6 (rc) a-a e{T+trd tsqr
v.mr ? a] €s-+ ERr
qTs-d cqro ({r{s E+"e ) strq 6t*
fr qr rrrrr*qr *r p.T.o.

589 t6

(iii) iMr dnr 6t{ vrrf esTrq (q6s E+Fc) 3:s-r {
F.}
fr eqr Rrr{{r l, oilsB- fur rqT * fr Et ffir nq"*
(oc) era ir-g+Ec fr-qr rrqr qr?
(c) e-qr fr ffi EsrF-d si{+ sre r'+. frftqier e} nn +i{r
*
fr o.r% ffi dqTf lr <)66 q] soo ffi sr+ iiinr* +
t* a* urar *r frfirfdT rn a +dr e fr- e-+fi ffi- +- a
t sTErfi ffi Aqquf rfi drfrr md Aa_tq q.r o,T+rr 6_{+,
fr+frtr{d +} an dfrqr

(i) qEfu6 w t =rc+ frq .rq trw fr dqTui ffi
fr 5w
*+ sfr wfr-qs1,
(ii) fiFqtaT Ero qRq + qt{ fr,q.rq_d er<r { q-t}
+t
xF-fittl

(iii) af-w enr m€E-c {qrg
tfr 61+ n Aqd rd+ fr
yrE-q-an

(fr+r rr+r * e4.25 - 0.77gg; e{.s : 0.6065:e{.r : 0.90g4)
Srer€|T

(m) qR rfi-{ s+ vfr rrqn * rarrfr.il (fuerq)
fr.qr rrqr *, tr qa
so cF{rfr rfl-sd aqa} tn.r Jf,ile'r qtfir qR zra
e_& rfiR
+ Re{rRd (fusTc) {fi fr .rS t * z16 40 cR$T
ff oqeil
6'r ysrer etfir fr-s+
Wrr{ E{fe * fr. so cR{ril {r{q_{q
(fusrc) vfi q-on t * .r{ d,

589 t7

(i) qR \1+. fiF-rrf, tcaTc * qra, 3-flrtrd c-64 a s-flrdt
+

i vrrq .rtqre ff rflzIT dlc{I + 3fu qra orffi vr<r
vrar t, A qfi-{ t-fi v-q,t t ranfr'd (fuorc)
A} m
qrfr"+.-f,r wr ti

(ii) qR {fr{ + q-6e a 3-nra A ff w i gsrFe frqt'
wr
A qfi{ sfr c-6n t r*{fiil (fuw) a+ m crkqil
e?

(re) unr< kd{qr + {onr{ fr fii dRqt

demanded
5. (a) The number of crates of ready-to-eat mangoes
demand in a period
and the frequency of each level of
of 200 daYs are given below:

No. of crates demanded 700 l'050
l'400 l'750

No. of daYs: 40 50 80 30

price of each
It costs Rs 250 to buy a erate. The selling
crate,ifsoldonthesamedayisRs400;butifitisnot,
value of Rs
the crate with the stale fruit has a salvage
l50.Howmanycratesshouldthedealerordereveryday
so that his profits may be maximised?
Also calculate
thc EVPI.

(b) Discuss various approaches to the
calculation of
(6+5)
probabititY.
P.T.O.

589 l8

OR

(a) (i) whar is fa*or reversar test? show that Fisher,s
index satisfies this test.

(ii) The probability that a house of a certain type will
catch fire during a year is 0.004. An insurance
company sells the owner of such a house
a Rs.
200,000 one_year term insurance poiicy for
a
premium of Rs 1.100. What is the
expected gain/
loss to the insurance company?

(b) (i) rne arithmetic mean of daily wages of 3c0 weavers
and 250 spinning machi'e Rorkers are
Rs r9g and
Rs 179 respectively. It is given that the arithmetic
nrean of all the workers in the factory
is Rs 1g7.
Find the total number of workers in the
factory if
it is also gir.,en that the arithmetic mean o1.the
dailv
wages of the rernaining workers is Rs
1g0.5.

(ii) An inr,estor buys shares of a company on three
days.
He invests equal amounts everyday and
buys shares
at the folloiving rates: Rs 24, Rs 30 and Rs
40.
Using an appropriate measure, calculate the
average
price paid by him. (6+5)

(q.) qrfr r$ t$-q-{z in+ fr ffi+. +1 Vtqr
\rq 200 fr{ fr
irsRr + rTr{r + n*r ar fr eKlqrdr fr+
fr .r$ *,

19
589
1,0S0 1,400 1,750
qffi rr{ arq,Rfr fr n{ql 7oo

Rfr fr ({qr
40 50 80 30

t' srft tr gfr Fa Arq frq
Frfr ffi fr oq f,rrRI 250
qr qet 400 n' ?; ifr-< qR W
qrt qt, e++. ffi Gr*q
srfr ffi qr ft6Rq rr€ 1s0 d'
{€t *dr A, rt Erfr s-&
ffir ffi qr entsr 2a uGv ilF 3t
?r *ot 6] vfrtr{
Ar tefteir€ qr ft qRq-f,{ *Rgt
B{nrq-fi dTt{ crq

+ RFra 5ffiql* m ssi frRet
Fe) crfr-{-dr
+ qRm.tr{ frTq

3TeIEn

*trq fr frrn qt
str'qur qtqvr wr li
c-dffi-d
(o.) (i) sqrcFr
{-Eq q-tar *r
q*6i-*^ {€ ctuoT 6}
ron * qt t erm drr* fr
(ii) sd + *tr+ ffi fifrTd fr
fiqr ffi g€ rs'R * s{ * €rfi
sTtro-dr o'ooa ?r
qt qq'-d ffiFr eg 200'000
t' fr €tqt
Itoo * fifuq
qr
qrft *r AqT 6qft anq-aR 3ltRrd
mRrfr qr frm-q
wr ii
efu zso 6n+fi
(Rfti qfr{) 6ffi fr
(rs) (l) soo gr+'t tmrzlf
?H6 qq$fr *
qqrm xltrl f-{!T: tss
^3tt qr qqrm qts
..{G$fr
rrqt * fr;t*+q {ft 6ffi fr
qR m fi Rqr ar{n e ffi tq 6m* m ?F6
187 e ?r
P'T'o'

s89 20

ru$d inr irqrir cTra 180.s a. * * *-r<qr+ +-
"rR,#
fr Aa {rdtr Elcr dfrgt
(ii) R-6 frarr*. fl-{ F{ \15. 6-+Tfr + m fr reffi 6-.dr
*r qa yR'tr{ cqr+ nM qiT fi+{r e,{dr * cfu za t
30 {. *r ao r. * Tgt* w iqr €fl-d-dr *r ofuc .rcrq
q.r .rc+{r 6{+, s{+ aRr r{rf,F{
fr.q rrq e*cc 1u q.r
cRq-ir+ dfrqr

(10,000)