tut problems 1

7/17/2019 Tut Problems 1

http://slidepdf.com/reader/full/tut-problems-1 1/7

Text Book: Complete Business Statistics (Aczel, Sounderpandian,

Saravanan, Joshi)-e

!evision o" Basics:

(1) The following data are scores on a management examination taken by a group of

22 people:

88,!,!",",2,#!,",#$,%8,$8,!$,##,#1,",!&,#8,$&,81,8#,"",8&,"1

'ind the median and the 2&th,%&th,!&th, and $&th percentiles

(2)uestion 1*%8 (page*2#) of text book

(%)uestion 1*## (page*"$) of text book

(")

+nclosed are box plots and some selected information on summary statistics ofreturn (in ) from two stocks -nswer parts 1a through 1d on the basis of this

-150

stock1

stock2



The coe.cient of /ariation of return for stock 1 is about 2 and the same for stock 2

is about 1& higher The standard de/iation of return for stock 1 is only about #

of that for stock 2 The median return for stock1 is about 1 unit lower than the

mean

("a) 0hich of the two stock returns is more skewed (and in what direction)

("b) ist numerical /alues (e/en if approximately) for any two measures of central

tendency and three measure of (absolute, not relati/e) dispersion of returns from

stock1 and stock2 (you need to pro/ide the name of the measures, as well) 34ou

may not count standard de/iation as well as /ariance as 2 di5erent measures6

("c)

7o of high outliers from stock 1 return:

7o of minor outliers from stock 2 returns:

7o of maor outliers from stock 2 returns:

()



(a) 9ean (b) nter uartile range (c) 9edian (d) ;ange (e) 7o of maor outliers

(f) <tandard =e/iation

(!) There are 8& new obs opening up at an airplane manufacturing plant, but 11&&

applicants show up for the 8& positions To select the best 8& from among the

applicants, the prospecti/e employer gi/es a combined physical and written

aptitude test The mean score on this test turns out to be 1# with standard

de/iation of 1& >an a person who scored 21 count on getting himself a ob (?se

>hebyshe/@s theorem)

(#) The law regulating producers of $*ounce boxes of breakfast cereal asserts that

no more than & of the output of any brand of cereal is allowed to contain less

than 88 ounces Ane company markets a $*ounce box of >orn Bu.es, which is

packed by a machine in such a way that the boxes ha/e mean weight $& ounces,

with a standard de/iation of &&1 ounce s the company /iolating the mentioned

law (?se >hebyshe/@s theorem)



#ro$a$ilit% and Ba%es Theorem:

(8)uestion 2*21 (page*!#) of text book

($)uestion 2*22 (page*!#) of text book

(1&)uestion 2*2# (page*#1) of text book

(11) uestion 2*%& (page*#1) of text book

(12) uestion 2*%1 (page*#1) of text book

(1%) uestion 2*%$ (page*##) of text book

(1") uestion 2*"& (page*##) of text book

(1) uestion 2*"" (page*##) of text book

(1!) uestion 2*"8 (page*#8) of text book

(1#) uestion 2*%C 2*"C 2*# (page*8&) of text book

(18) uestion 2*8$C 2*$2 (page*$!) of text book

(1$) uestion 2*1&"C 2*1& (page*$8) of text book

(2&)

The year is 2&1 and ndia is playing in the 0est ndies ts chance of winning any

Test is &" and losing is &! (=rawn or tied Test 9atches are considered improbable

gi/en the recent pitch conditions in the 0est ndies)

(2&a) what is the probability that after the after the Drst four tests, the series is tied

at 2*2

(2&b) Ei/en that the Drst four Tests are tied 2*2, what is the probability that ndiawon the Drst and third Test

(21)

The Brime 9inister is worried about the rising oil prices in the nternational market

f he increases the domestic price of petrol and diesel, it will reduce the burden of

subsidy Fut inGation will go up t is estimated that %& of ndia is poor and,irrespecti/e of the le/el of inGation, the net social loss for them with the rise in

prices will be ;s1&& crores Then there is a /ulnerable section of " and they

would lose ;s1&&& crores The top 2 stood to gain ;s!!&& crores

(21a) The B9 decides to go ahead and raise domestic oil prices The politicalad/isors are now worried They estimate that 8& of the poor, !& of the



/ulnerable section and 2& of the well o5 will not /ote for the ruling party 0hat isthe probability of someone /oting for the ruling party if there is an election(21b) +lections are indeed held f a person chosen at random has not /oted for theruling party, what is the probability he is from the poor

(21c) if a person is not a beneDciary of the oil price rise, what is the probability he

will not /ote for the ruling party

(22)

<anath Hayasuriya hits a six on any ball he faces with probability &1

(22a)0hat is the probability he will hit at least one six in a ! ball o/er

<ri anka needs 12 runs in the last four balls and Hayasuriya is batting -ssume that

he does not get out, and either hits a six or misses each ball

(22b) what is the probability that they win o5 the last ball

(22c) what is the probability that they win

(2%)

Af the Drst year students at a 9I, it is known that !& are engineers The BEBo.ce reports that %& of the non* engineers maintained an - a/erage duringtheir Drst year at the college and that 2 of all Drst year students maintained an- a/erage

2%a) f a student has - a/erage, what is the probability that the student is anengineer

2%b) -re the e/ents - a/erage and engineer

(i) 9utually exclusi/e (ii) ndependent

+xplain your answer in each case

(2")

Three clerks, I, 4 and J, all write special orders at a bookstore 9r I writes &

of all special ordersC 9r 4 writes 2& and 9r J writes %& 0e also know that 9rI makes a mistake on 1 out of 1&& ordersC 4 makes a mistake " of the time andJ makes a mistake 2 of the time - customerrecei/es the wrong book and correctly maintains that there was a mistake in takingthe order &hat are the prior and posterior pro$a$ilities that 'r *rotethe order+

()



7< 9etallurgical ndustries td manufactures special castings for the automobile

industry <wetha, the Broduction 9anager, is re/iewing the Kuality of their castings

There are only two possible defects in the castings, namely L typeM and LJ typeM

(only one of them can occur in a gi/en casting) Fased on her past experience,

there is a 1& chance of L typeM defect and a 2& chance of LJ typeM defect

occurring in the castings The Kuality control department (>) reects the castingsbefore they lea/e the factory, if they can detect either of the defects Fased on the

past data they reect the castings with the L typeM defects & per cent of the time

and those with LJ typeM defects, only 1& per cent of the time <ometimes, the >

reects the castings without either of the defects and this happens percent of the

time

Fased on the abo/e, answer the following Kuestions:

(2a) if one casting is selected at random, what is the probability that it has LtypeM defect and also the casting is reected by >

(2b) what is the probability that a casting selected at random is reected

(2c) if a casting is not reected by the >, what is the probability that it has LJtypeM defect

(2!)

9r Earib Nhan, 9arketing 9anager in*charge of <oft white detergent is exploringthe possibility of ad/ertising his product on the upcoming >hampions@ Trophy

Tournament of A=s Ois ad/ertising agency has informed him that the regular slots(between o/ers) ha/e already been taken, but Lspecial slotsM are still a/ailable

These are the slots a/ailable when wickets fall 0ith his long experience, he knowsthat the /iewers@ intensity is strong during the Drst hour that ndia is batting fndia is batting and or more of wickets fall in the Drst hour, <oft white will ha/eOigh +xposure (LOow unpatriotic, but that is lifeM, he told himself) f less than D/ewickets fall during the Drst hour, <oft white will ha/e ow exposure Oe also knowsthat the probabilities di5er depending on whether ndia is batting Drst or DeldingDrst Oe has estimated that the probability of or more ndian wickets falling, whenndia is batting Drst is &"& An the other hand if ndia is batting second (ie,Delding Drst) then the probability of or more wickets falling is higher at &#& Oerightly assumed that the probability of ndia winning the toss is &Af course, whether ndia is bating Drst or Delding Drst depends on ndia winning the

toss, which is completely unbiased Bast data indicates that in similar tournaments,

ndia elected to bat 8& of the time after winning the toss An the other hand,ndia was put to bat only %& of the time when they lost the toss

(2!a) what is the oint probability that ndia wins the toss A./ elects to bat Drst

(2!b) what is the oint probability that ndia loses the toss A./ elects to bat Drst

(2!c) what is the probability that ndia bats Drst

tut problems 1

Documents