Theoretical Distributions In Business Statistics 15 October

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STATISTICS & BUSINESS PROBLEMS

AFTERSCHO☺OL – DEVELOPING CHANGE MAKERS

CENTRE FOR SOCIAL ENTREPRENEURSHIP PGPSE PROGRAMME –

World’ Most Comprehensive programme in social entrepreneurship & spiritual entrepreneurship

OPEN FOR ALL FREE FOR ALL

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STATISTICS & BUSINESS PROBLEMS

Dr. T.K. Jain.

AFTERSCHO☺OLCentre for social entrepreneurship

Bikaner M: 9414430763tkjainbkn@yahoo.co.in

www.afterschool.tk, www.afterschoool.tk

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Find the binomial distribution if the mean is 48 standard deviation is 4.

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P(A) =1/3, P(B) = ½, P(A-B) = 1/5, what is the probability that only B

will happen?

• P(A) = 1/3 (WHICH INCLUDES A+B ALSO).

• P(A-B) = 1/5 (ONLY A – BECAUSE HERE B IS EXCLUDED)

• P(A &B) (Together) = 1/3-1/5 = 2/15• P(ONLY B) = ½ - 2/15 = 11/30 ans.

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What is the probability that 4 children selected at random would

have different birthdays?

• For the first boy there are 365 choices, for second, there are 364 choices, for third there are 363 choices and for 4th there are 362 choices. Thus the probability is

• (365*364*363*362) / (365^4) = .983644 answer

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There are 3 boxes with following details: Box 1. (5 red,7 white, 6

blue) box 2: (4red,8 white,6 blue), box III : (3 red,4 white,2 blue), if one ball is drawn at random from

each of these, what is the probability that we have 3 balls of

same colour?

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Solution.

• Let us assume that we get Red from each: • 5/18*4/18* 3/9 = 60/2916• For white : • 7/18*8/18*4/9 = 224 /2916• For blue: • 6/18*6/18*2/9 = 72/2916• = 356/2916 : = .122 ans.

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What is the probability that a leap year selected at random will have

53 Saturdays?

• We have 52 week plus one extra day in a normal year. This extra day can be any one from Mon. to Sun. In leap year, we have 2 extra days thus we can have these 2 extra days on any of MON+Tue or any combination of 2 days.

• Thus we have 2/7 probability that the leap year will have 53 Saturday. Ans.

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A pocket of 10 components include 3 defectives. If 4 components are

selected from the pocket at random, what is the expected value

of the number of defectives? 0 1 2 3

7c4/10c4

7c3*3c1/10c4

7c2*3c2/10c4

7c1*3c3/10c4

.167 .5 .3 .0330 .5 .6 .099 1.199

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30% failed in Acct. 40% failed in Eco and 50% failed in at least one

of these papers. If we randomly pick up a person, who is failed in Eco,what is the probability that he

has passed Acct? • Let us find the % for those who have failed

in both the papers. • 30+40 – X = 50• X = 20 thus there is 50% probability that

he has passed Accts.

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A problem was given to Mayank, Goti and Nidhi (pgpse students),

the probability they will solve is 1/3, 1/5 and ½, what is the probability that the problem will be solved?

• Let us assume that Mayank doesn’t solve it: 2/3, Goti doesn’t solve it 4/5 and Nidhi also doesn’t solve it ½. All 3 don’t solve it :

• 2/3*4/5*1/2 = 8/30. thus problem will be solved : 22/30 or 11/15 answer.

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If NC2 = NC5, what is N ?

• N = 2+5 = 7• Thus N = 7 ans.

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How many numbers of 5 digits can be formed with 0,1,2,3,4,6,8?

• For the first digit we have 6 options, for 2nd digit we have 6 options (the digit used earlier will not be used), for 3rd digit we have 5 options, and for 4th digit we have 4 options and for last 5th digit we have 3 options). Multiply all these to get the answer:

• =6*6*5*4*3*• =2160 answer. • If repetition is allowed: • 6*7*7*7*7• =14406 ans.

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There are 2 boxes. The first contains 3 red and 5 white balls.

The 2nd contains 4 red and 6 white ball. One ball is taken from first box and transferred to 2nd box. And then

another ball is drawn from the second box. What is the probability

that the second ball is Red?

• Let us assume that we draw red ball from first box and then we have 5 red in 2nd box

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Solution ….• 3/8 *5/11 = 15/88• Suppose we draw white ball from first box: • 5/8*4/11 = 20/88 (multiply because there is &

between them). • Now add these two: • 35/88 answer. (add because there is OR

between them). • (in first possibility, we have red ball from the first

box and again red ball from 2nd box. In 2nd possibility, we have white from 1st and red from 2nd box.).

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ABOUT AFTERSCHO☺OL

Afterschoool conducts three year integrated PGPSE (after class 12th along with IAS / CA / CS) and 18 month PGPSE (Post Graduate Programme in Social Entrepreneurship) along with preparation for CS / CFP / CFA /CMA / FRM. This course is also available online also. It also conducts workshops on social entrepreneurship in schools and colleges all over India – start social entrepreneurship club in your institution today with the help from afterschoool and help us in developing society.

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Why such a programme?

• To promote people to take up entrepreneurship and help develop the society

• To enable people to take up franchising and other such options to start a business / social development project

• To enable people to take up social development as their mission

• To enable people to promote spirituality and positive thinking in the world

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Who are our supporters?

• Afterschoolians, our past beneficiaries, entrepreneurs and social entrepreneurs are supporting us.

• You can also support us – not necessarily by money – but by being promotor of our concept and our ideas.

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About AFTERSCHO☺OL PGPSE – the best programme for developing great

entrepreneurs• Most flexible, adaptive but rigorous programme• Available in distance learning mode• Case study focused- latest cases • Industry oriented practical curriculum• Designed to make you entrepreneurs – not just

an employee• Option to take up part time job – so earn while

you learn • The only absolutely free course on internet

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Workshops from AFTERSCHO☺OL

• IIF, Delhi• CIPS, Jaipur• ICSI Hyderabad Branch• Gyan Vihar, Jaipur• Apex Institute of Management, Jaipur• Aravali Institute of Management, Jodhpur• Xavier Institute of Management, Bhubaneshwar • Pacific Institute, Udaipur• Engineering College, Hyderabad

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Flexible Specialisations:• Spiritualising business and society• Rural development and transformation• HRD and Education, Social Development• NGO and voluntary work• Investment analysis,microfinance and inclusion • Retail sector, BPO, KPO• Accounting & Information system (with CA / CS /CMA)• Hospital management and Health care• Hospitality sector and culture and heritage• Other sectors of high growth, high technology and social

relevance

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Salient features:• The only programme of its kind (in the whole world)• No publicity and low profile course• For those who want to achieve success in life – not just a

degree• Flexible – you may stay for a month and continue the rest of

the education by distance mode. / you may attend weekend classes

• Scholarships for those from poor economic background• Latest and constantly changing curriculum – keeping pace

with the time• Placement for those who are interested• Admissions open throughout the year • Latest and most advanced technologies, books and study

material

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Components • Pedagogy curriculum and approach based on IIM Ahmedabad and ISB

Hyderabad (the founder is alumnus from IIMA & ISB Hyderabad)• Meditation, spiritualisation, and self development • Essential softwares for business• Business plan, Research projects• Participation in conferences / seminars• Workshops on leadership, team building etc. • Written submissions of research projects/articles / papers• Interview of entrepreneurs, writing biographies of entrepreneurs• Editing of journals / newsletters• Consultancy / research projects • Assignments, communication skill workshops• Participation in conferences and seminars• Group discussions, mock interviews, self development diaryng • Mind Power Training & writing workshop (by Dr. T.K.Jain)

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Pedagogy • Case analysis,• Articles from Harvard Business Review • Quiz, seminars, workshops, games, • Visits to entrepreneurs and industrial visits• Presentations, Latest audio-visuals• Group discussions and group projects• Periodic self assessment• Mentoring and counselling• Study exchange programme (with institutions out of

India)• Rural development / Social welfare projects

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Branches

• AFTERSCHO☺OL will shortly open its branches in important cities in India including Delhi, Kota, Mumbai, Gurgaon and other important cities. Afterschooolians will be responsible for managing and developing these branches – and for promoting social entrepreneurs.

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Case Studies

• We want to write case studies on social entrepreneurs, first generation entrepreneurs, ethical entrepreneurs. Please help us in this process. Help us to be in touch with entrepreneurs, so that we may develop entrepreneurs.

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Basic values at AFTERSCHO☺OL

• Share to learn more• Interact to develop yourself• Fear is your worst enemy• Make mistakes to learn • Study & discuss in a group• Criticism is the healthy route to mutual support

and help • Ask fundamental questions : why, when, how &

where?• Embrace change – and compete with yourself

only

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society