University of Delhi 2010-1st Year B.Com (Hon.) Marketing Management (HONS) BUSINESS STATISTICS UNIVERSITY - Question Paper
BUSINESS STASTISTICS PAPER 6004
I B.Com. (Hons.)/I J
f
Paper IVBUSINESS STATISTICS (New Course : Admissions of 2004 and onwards)
Time : 3 Hours Maximum Marks 75
W? : 3 Tjqfe : 75
(Write your Roll No on the top immediat&y on receipt of this question paper,)
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Note : The maximum marks printed or the question paper are applicable for the candidates registered with [he School of Open Learning for the B.A.(Hons.)/B Com.(Hons.). Thes; marks will, however, be scaled down proportionately in respect of the jtudents of regular colleges, at the time of posting of awards for compilation of result.
Note Answers may be written either in English or in Hindi, but the same medium should be used througlout the paper.
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Attempt All
uestions
Use of simple calfcuator is allowed.
. . f Logarithmic tables and graphs will be supplied on demand.
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1. (a) Comment on any three of the following :
(0 In a factory outlet a unit of work is completed by A in 10 minutes,
\
by B in 15 minutes, by C in 16 mmutes and by D in 20 minutes. What is the average number of units of work completed per minute ?
(ii) What is relative frequency approach of probability ?
(iii) Standard deviation may be negative or positive.
i
(iv) State the tests that tre used to determine the presence of skewness in a distribution
(b) The first four central moments of a distribution are 0, 16, -36 and 120
pon the Skewness and Kurtosis of the
respectively. Comment distribution.
Or
Write a short note on BSE SENSEX
(c) Are the following statemeits True or False ? Give reasons :
() If the coefficient of correlation between two variables X and
t
i
Y is 0.8, then coeficient of correlation between X and -Y
is --0.8. t
t
(ii) If the coefficient of (brrelation between X and Y is perfect, the two lines of regression of X on Y and Y on X are reversible.
(i) <*k<A 3 A 10 Pro 3 TJJT %, B 15 fw 3, C 16 f*R3 3 afa D 20 ftTC 3 I sftl Pro
afcra crt | ?
(ii) mPiqrai r antfsra? 3nfri win w | ? (iu) tutr; Pw<?h ww arw It toit % i
(iv) *Z=l 3 fc**T ?& PcRJHUdl ftqffet cfi. cjf TJT
(T) (CT V&tjK f=T 3r?T: 0, 16, -36 afa 120 ? I T
< ni <i*n cfjir fepift tfl&m i '
(0 tb . 3to y $ ?i??Erasi ipiR> o.8 t, ra -x afk -y
y I '
(ii) 7R X ' Y ijpf Tjori-1; (RY'RX WX
2. (a) The coefficient of correlation between ages of husbands and wives in a community was found to be +0.8, the average of the husbands* age was 25 years and that, of wives age was 22 years Their standard deviations were 4 and 5 respectively. Find with the help of regression equations :
(i) The expected age of the husband when wifes age is 18 years, and v
i
i
(ii) The expected age of the wife when husbands age is 32 years.
t
(b) The trend equation for quarterly Wes of a firm is estimated to be as ;
Y = 20 + 2X, where Y is sales per qijter in millions of rupees, unit of X is one quarter and the origin is ndle of the first quarter (Jan.-March) of 2005. The seasonal indices ofles for the four quarters are given below :
I
i\
Quarter : I II II , jy
Seasonal Indices : 120 105 *
Estimate the actual sales for each quartet2010.
(c) A textile worker in a city earns Rs. 3,655 per month. The cost of living index for a particular month is 145. Find the amount of money I he spends on house rent and clothing with the help of below given information .
|
Group |
Expenditure |
Group Index |
|
Food |
1400 |
180 |
|
Clothing |
? |
150 |
|
House Rent |
? |
100 |
|
Fuel & Lightmg |
555 |
110 |
|
Miscellaneous |
640 |
91 |
5+5+5
(=f) fa 3 sngaif cfr +0.8 t,
/ 4 5 *t I y41<+><uli $ Ulcf
(i) Mfro aurg cfit sng 18 t, afa
() wnftra siq 4 aiig 32 % i
(g) firing faaft sjir ttsr % :
Y = 20 + 2X, Y ft#PH 3 TjftT fcWlst faslft t, X
| 3f(k TJcT 2005 fall# (*Hg$-TJp{) W | |
120 105 85 90 2010 3fiS fiWTWt c|R<tfW ft T 3TRR fali |
(n) V& 3 v$ *farc 3,655 ? rar I fafa frafe-ra 3>i+ 145 t i if w*rar $ iro 3?R'-r|f tR ti| xiftr ra ffisrci .*
|
wra | ||
|
<il5R |
1400 |
180 |
|
? |
150 \ \ | |
|
TOR pOTPfl |
? |
100 \ |
|
f*H S+IVI 4cR*|| |
555 |
110 v |
|
640 |
91 \ |
Or
(a) Explain the properties of Regression Coefficients.
(b) Given below is the information relating to a bivariate distribution :
Regression equation Y on X : Yc = 20 + 0.4X, Mean of X = 30, and Correlation coefficient between X and Y = 0.8.
Find regression equation of X on Y.
(c) A box of 100 gaskets contains 10 gaskets with type A defect, 5 gaskets with type B defect and 2 gaskets with both types of defect.
Find the probabilities that :
(i) a gasket to be drawn has a type B defect under the condition that it has a type A defect, and
*
(ii) a gasket to be drawn has no type of defect under the condition,
that it has no typf A defect. 5+5+5
(cB) TO
(73) -=fr% 133? t % :
XlYfl : Yc = 20 + 0.4X, X >1 = 30
= 0.8 I
y x 'swispto h)<*k|ji i
(iT) 100 ft' 3 10 A Tfft t, 5 B 2 3 nf tok f i gitoviT fj :
(i) A $ faro sfcnfa tir6z if b
(u) <A SfirfcT W&Z 3
ychR |f % I
( 8 ) 6004
3. (a) Write the mathematical properties of standard deviation.
(6) Fmd the coefficient of correlation Jbetween age and playing habits of the following students .
No. of students : 2500 2000 1500 1200 1000 800
r
Regular players : 2250 1200 1050 480 250 120
Age of players : 16 17 18 19 20 21
(c) Under an employment promotion programme, it is proposed to allow sale of newspapers on the buses during off peak hours The vendor can purchase the newspaper at a special rate of Rs. 1.25 per copy and sell
* it for a price of Rs. 1,60. Any unsold copies are treated a dead loss.
A vendor has estimated the folowing probability distribution for the number of copies demanded dinng 150 days :
Number of copies : 15 1 16 17 18 19 20
I
Number of days : 10 25 35 40 25 15
i
How many copies the vendor sbuld buy for maximum gam ? Also, calculate EYPI. I 5+5+5
(1) fHHfirlRslil if rpri'c*,
wsif WIT : 2500 20 1500 1200 1000 800
fcqftH : 2250 13 1050 480 250 120
( 9 ) 6004
(T) Ml chl4st>H # STcTfcT TB TClf 3 3HJst(l<i
fagft sqqfa 1 JIM3 I I 1.25 '5lRt
-snaR Tarte 1.60 ? ui% n % I 4i[<sti1fl ufirat TJJJi '5lf% 'tlRI 'H<<il I yen q'l qi<ji % 150 itt 3jfoii fen fanfafisra wiPj+di aiRrfi
HftNf, : 15 16 17 18 19 20
f&f HSIT : 10 25 35 40 25 15
cn*i fnj; =n ? eypi
Or
() Write a short note on Bayes Theorem.
() A computer while calculating the coefficient of correlation between the variables X and Y derived the following results :
N = 30, EX = 120, ZX2 = 600, SY = 90, 2Y2 = 250, ZXY = 335.
It was later discovered that the computer copied down two pairs of observation, as :
X 8 12 '
Y 10 7
whereas the correct values were
X 8. 10
Y 12 8
Compute the correct coefficient of* correlation between X and Y.
(c) The sales of a company for the year 2003 to 2009 are given below : Years : 2003 2004 2005 2006 2007 2008 2009
Sales (in millions) : 32 47 65 92 190 132 275
/
Estimate sales for the year 2012 with the help of exponential
curve (Y = ABX). 5+5+5
O) -q* Mm, i
(13) rHHfafad
mR*jih W<\ :
N = 30, IX = 120, SX2 = 600, IY = 90, IY2 = 250, 2XY = 335.
X 8 12
Y 10 7 *TH :
X 8 10
Y 12 8
t y
x % y irst guifa? srfqRfpi i
(T) 2003 2009 t :
s 2003 2004 2005 2006 2007 2008 2009
teA Tf) : 32 47 65 92 190 132 275
RHRlHl (Y = AB?) 2012 3nR
fclfaiJ. I
4. (a) If 5% students appearing in an examination fail, using Poisson distribution find the probability that out of 100 students appearing in the examination :
(i) none failed,
(ii) 5 students failed, and
(iu) maximum 3 failed
(6) The production of a commodity. during 2005>2010 is given below. Fit ,the second degree parabola curve and estimate the production for the year 2014 :
Year : 200? 2006 2007 2008 2009 2010
Prod. (000 tons.) : 10 12 15 16 18 21
7+8
%
(0 Tjfe 'Rtsn s% "m aipH t, '31
?RI 100 $ :
I
(T3) 2005-2010 f=TR 3J3>n pn I ft?fa
wrfm +Un aik 2014 rfWKH grt snwr
ftfTT :
: 2005 2006 2007 2008 2009 2010
(000 i 10 12 15 16 18 21
Or
() A project yields an average cash-flow of Rs. 550 lakhs and standard deviation cash flow of Rs. 110. Calculate the following probabilities assuming the normal distribution
(i) Cash flow will be more than Rs. 675 lakhs.
(ii) Cash flow will be less than Rs. 450 lakhs.
(iii) Cash flow will be between Rs 425 lakhs and Rs. 750 lakhs.
() From the following quarterly prices of Coke for six years, calculate seasonal variations by the method of ratio-to-moving average :
(<?)) 550 <riio Hi-nn H{1 wqts 3 HiTich
Traif 110 c# % I TOWHf |HJ PinR-lfad
HlRM>dl3if 3?T MfidxrH <*>11*113. :
(t) =wt rar? 675 ? 3 srftre; mt,
(m) =lt Trai? 425 eTR3 sfa 750 cW ?. *fN ?f>TT I
(13) W. crof [HHRrlfiskl fiwi# 3gcfRT--i|fdMH 31
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5. (a) If a machine is correctly set-up it produces 90% acceptable items. If it is incorrectly set-up it produces 40% acceptable items Experience shows that 80% of the set-ups are correctly done.
(i) If after a certain set-up, out of the first two items produced, first is found to be acceptable and second unacceptable, what is the probability that the machine is correctly set-up ?
(ii) If the machine produced first two items as acceptable, what is the probability that the machine is correctly set-up ?
c
(6) In a partially destroyed laboratory record, the following results are only legible :
Variance of X = 9,
Regression equations;
8X - 10Y = -66, 10X - 4 5Y = 53 5.
Find :
(i) the standard error of estimate between X and Y and Y and X, () the standard deviation of Y, and
{iii) the coefficient of correlation between X and Y. 7+8
0?0 (Ft) tpc 90% crcg lift'd
% I H 'jii 40% wlchi<f drniRo <til % I
arpra iRi gHT t % 80% 4iwim bNt f i
(i) 13 swim TR, ii -q?# cRgaff i} qif wifa+di % % 3hs $ eimf Tif % ?
(ii) H*i)l jJRT flf M&i) qjt wl*hi4 Ilf 7Tf (it Mi(<<<t>ttl t far Trcto b1=f 3 cpnf t ?
(g) 3tot: to sj4l*midi arfrar 3 ?r faHfdRsid vre t :
X WT = 9
8X - 10Y = -66, 10X - 4.5Y = 53.5.
*lld 'tOfiny, :
(i) x ak Y mT Y ak x $ gfe,
(ii) Y RTOJ feWcM, 3?fc
(iii) xiY#9 JpTO I
Or
(a) A toy company is planning to introduce few changes in the toys under three categories; complete change, partial change and minimum change. Further, the company has three levels of product acceptance. Management will make its decision on the basis of expected profits
from the first year of production. The relevant information are give below .
Anticipated 1st year profits (Rs. 000) Product acceptance Complete change Partial change Minimum change
Good 80 70 50
Fair 50 45 40
Poor (25) (10) 0
You are asked to take an optimal decision on the basis of the following decision criteria :
(i) Minimax,
(ii) Maximax,
i
(idi) Maximh,
(iu) Laplace, and (i>) Hurwicz
assuming the sssimism index as 0.35.
50
40
0
50
(25)
(b) The first four moments of a distribution about the value 5 of the variables are 2, 20, 40 and 50 Calculate the mean, variance, pj and p2 and comment upon the nature of distribution. , 8+7
(30 133? fisleflHI StM - TJjf -qtexN,
ak aicpfa r=n % a#c
cbHHl 3cHK;-*q)'t><.ul W f I TiT
$ CHS airaR M*? i nf t ;
yrmRfid (ooo .)
Tjpf nRc<<k 80
0 35 fl'Rct fHHid Rsttf 3um tR srggpcPT frfa eftr | :
(1) SlrrmfW,
(u) irf|Tgqfpg;
(m)
(iv) cwra, aift (y) f5R5T |
() t| TIH 5 i<n 3 2, 20, 40 3fr( 50
t I TWI, '5RRDI, pj 3fa P2 mR-sIcRI 3fa fe TR
70
45
(10)
6004
16
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Attachment: |
| Earning: Approval pending. |
