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Decision Science

September 2023 Examination

 

 

Q 1: Determine the probabilities for the below given statements and write your interpretation using following data.   (10 Marks)

 

 

 

		Do you like Anupama?
		No	Yes	Total
Do you like ‘Kyuki sas bhi kabhi bahu thi”?	No	15	5	20
	Yes	5	25	30
	Total	20	30	50

 

 

1.   What is the probability that randomly selected person has said “yes, I like Kyuki…”?

 

 

2.   What is the probability that randomly selected person has said “ I don’t like Kyuki…”?

 

 

3.   What is the probability that randomly selected person has said “yes, I like Anupama…”?

 

4.  What is the probability that randomly selected person has said “ I don’t like Arupama…”?

 

5. What is the probability that randomly selected person has said ‘like Anupama’, also said

 

‘like kyuki….’ prior to that?

 

6.  What is the probability that randomly selected person has said ‘like Kyuki….’, also said

 

“don’t like Anupama” prior to that?

 

Note: Do not use any software for the calculation, you are advised to show all necessary steps of calculations.

 

Ans 1

1. Probability of saying "Yes, I like Kyuki...”

This change can be determined by dividing the number of those who said "sure," like Kyuki, by the whole number of human beings:

 

Probability = (number of those who said "yes” like Yuki) / (general number of humans)

 

Probability = 30/ 50 = 0.6 or 60%

 

Interpretation: The possibility that a

 

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Q2: Calculate the correlations among all possible combinations of variables using the following data and write your interpretations.   (10 Marks)

 

 

 

 

State	Urban No of Bank Offices	Urban Amount Credit	Urban Amount Deposit	Urban No of Accounts
ANDAMAN & NICOBAR ISLANDS	31	10798.91	23009.661	300860
ANDHRA PRADESH	4254	1771561.22	1785273.21	56997520
ARUNACHAL PRADESH	71	18713.635	55093.574	620951
ASSAM	1164	321567.825	807884.938	15333369
BIHAR	3056	559501.655	1812236.67	42338127
CHANDIGARH	424	585840	549184	3364488
CHHATTISGARH	1284	599595.538	848908.706	15436631
DADRA & NAGAR HAVELI	35	9937.519	26367.337	488036
DAMAN & DIU	43	8227.23	36462.355	473049
GOA	397	126414.224	433800.37	3640393
GUJARAT	4831	3619277.92	4567644.04	60961143
HARYANA	2905	1446481.5	2226409.05	31466846
HIMACHAL PRADESH	381	90320.203	271842.575	2927090
JAMMU & KASHMIR	819	239474.898	578992.602	8568486
JHARKHAND	1501	385210.622	1302088.44	17698133
KARNATAKA	6204	4337559.3	6418221.89	72858087
KERALA	5949	2212958.59	3575806.38	59406050
LAKSHADWEEP	5	413.064	4906.115	34583
MADHYA PRADESH	3901	1447929.15	2508450.77	56132871
MAHARASHTRA	8846	21914275.1	21203097.7	139566919
MANIPUR	84	17502.179	47232.768	1216224
MEGHALAYA	165	30045.858	141589.032	1134644
MIZORAM	102	20101.754	51840.488	743615
NAGALAND	102	21505.157	70089.604	871327
NCT OF DELHI	3408	9559956.37	9604406.95	43749602
ODISHA	2123	678962.946	1608027.32	21675814
PUDUCHERRY	180	75818.599	118598.454	1989219
PUNJAB	3681	1547952.7	2283001.19	35795072
RAJASTHAN	3988	1475735.94	2194328.32	45786526
SIKKIM	39	10980.099	42445.246	303941
TAMIL NADU	7218	6172405.9	5455337.41	89424694
TELANGANA	3296	3359268.45	3303802.62	43319782
TRIPURA	216	41708.593	127616.832	2685808
UTTAR PRADESH	8522	2490881.56	5930432.61	117339360
UTTARAKHAND	1042	251706.35	748447.406	8992680
WEST BENGAL	4498	3061581	5141434.75	65921120

 

 

 

 

Ans 2 (A)

The correlation coefficient between "urban No of bank offices" and "city amount credit," primarily based on the records analysis in Excel, is zero.684. This shows a moderate positive

The correlation coefficient between "Urban No of Bank Offices" and "Urban no of Amount"

The correlation coefficient between "urban No of bank offices" and "urban No of accounts" based on the analysis of the facts in Excel is 0.984. This indicates a robust and high-quality

The correlation analysis in Excel was famous for a robust positive correlation between the variables "urban quantity" (urban amount) and "credit" (credit). The correlation coefficient of one indicates a perfect delicate linear relationship among those variables. This suggests that

The correlation evaluation in Excel reveals a high-quality correlation between the variables

 

 

 

Q 3A: In Maharashtra there are 20 Big companies in IT sector. Out of these, 15 companies are in Mumbai. What is probability that at least two companies are from Mumbai if total 3 companies selected randomly to form a sample.     (5 Marks)

Note: Do not use any software for the calculation, you are advised to show all necessary steps of calculations.

 

Ans 3A:

Solution

To solve this problem the use of the binomial distribution, we can define the following parameters:

 

Q 3B: Draw the Line chart using EXCEL for the following variables and write your interpretations. Looking at the graph/ numbers (in the table) what type of correlation is suspected between crop area of wheat and cereals.    (5 Marks)

 

 

Year	AREA UNDER CULTIVATION Wheat (Lakh hectares)	AREA UNDER CULTIVATION Coarse Cereals (Lakh hectares)
1965-66	126	443
1970-71	182	460
1975-76	205	438
1980-81	223	418
1985-86	230	395
1990-91	242	363
1995-96	250	309
2000-01	257	303
2005-06	265	291
2010-11	291	283
2015-16	304	244
2020-21	311	241

 

 

 

Ans 3B:

The graph displays the crop area of wheat and coarse cereals over a span of several years, ranging from 1965-66 to 2020-21. by using studying the graph, we can observe a clear pattern and draw conclusions about the correlation between those  variables.

First, let's focus at the crop area of wheat. From the initial year of 1965-66 to the final year of