# NMIMS DEC 2021 DECISION SCIENCE

DECISION SCIENCE

1. Calculate the probabilities for the following statements as per the given scenario and draw the probability tree diagram also (Note: This diagram can be prepared in MS-Paint or manually).

A study undertaken by the Rajan Supervisor of Elections in 2002 revealed that 44% of registered voters are ‘Dharwadi Yuth’, 37% are Rajmoti, and 19% are others. If two registered voters are selected at random, what is the probability that both of them have the same party affiliation?

2. Calculate the correlation between pairs (recommended below) of the following variables and write interpretation for each correlation coefficient. (Note: For the following pairs, correlation can be calculated using EXCEL.)

Recommended Pairs:

1. Correlation between ‘number of female migrants for work/ employment’ v/s ‘Number of male migrants for work/ employment
2. Correlation between ‘number of female migrants _ Education’ v/s ‘Number of male migrants _ Education’
3. Correlation between ‘number of female migrants _ Business’ v/s ‘Number of male migrants _ Business’
4. Correlation between ‘number of female migrants _ Marriage’ v/s ‘Number of male migrants _ marriage’

Table: State to state migration with reasons of migration as per census 2011.

 Work/empl oyment Busi ness Educa tion Marr iage Work/empl oyment Busi ness Educa tion Marr iage State _name Females Fem ales Femal es Fema les Male Male Male Male JAMMU & KASHMIR (01) 4,911 495 1,085 43,13 0 22,716 1,985 1,762 1,372 HIMACHA L PRADESH (02) 13,938 493 3,200 1,08,1 53 95,255 3,188 5,647 1,932 PUNJAB (03) 72,829 5,468 5,757 6,92,4 59 5,16,724 11,29 5 10,228 15,13 9 CHANDIG ARH (04) 14,435 787 8,725 1,06,7 74 1,85,856 7,463 13,769 1,290 UTTARAK HAND (05) 25,691 1,733 7,717 3,64,6 98 2,65,536 6,530 19,304 4,913 HARYANA (06) 1,05,741 6,670 8,047 12,84, 022 6,77,595 14,66 5 12,805 23,72 2 NCT OF DELHI (07) 1,19,575 7,610 23,224 12,01, 945 18,14,435 39,05 1 73,391 15,65 4 RAJASTH AN (08) 49,392 4,192 13,275 12,88, 934 3,29,428 9,374 18,313 13,81 0 UTTAR PRADESH (09) 91,265 14,57 8 12,649 20,52, 928 4,35,014 19,47 3 36,835 30,90 7 BIHAR (10) 12,127 2,371 2,105 7,99,3 73 45,028 2,959 3,258 15,27 5 SIKKIM (11) 2,616 257 698 14,76 4 16,926 2,617 925 331 ARUNACH AL PRADESH (12) 8,260 1,104 599 18,96 2 41,110 8,613 928 319 NAGALAN D (13) 4,420 921 1,103 15,30 7 28,567 9,993 1,783 471 MANIPUR (14) 419 267 321 5,378 1,804 1,801 520 185 MIZORAM (15) 1,795 209 361 2,522 9,918 1,009 446 424 TRIPURA (16) 6,795 143 149 17,50 2 15,891 955 283 578 MEGHALA YA (17) 2,726 403 1,878 25,46 9 17,727 4,407 3,025 4,418 ASSAM (18) 6,642 2,378 1,834 1,56,1 84 74,921 49,69 7 3,074 5,495 WEST BENGAL (19) 36,504 7,436 5,567 7,49,9 96 4,32,269 76,03 6 15,470 23,67 6 JHARKHA ND (20) 31,154 4,061 5,872 9,84,4 64 3,83,816 16,09 4 15,672 25,10 1 ODISHA (21) 11,709 3,735 4,935 3,27,4 76 1,11,038 40,91 7 10,369 9,282 CHHATTIS GARH (22) 29,610 1,843 3,160 4,01,9 47 2,69,311 11,21 3 7,196 11,43 6 MADHYA PRADESH (23) 52,026 7,859 9,221 12,87, 527 3,86,776 15,60 9 22,575 27,46 0 GUJARAT (24) 75,552 18,86 5 5,722 6,28,4 73 10,46,192 1,23, 091 12,864 17,92 8 DAMAN & DIU (25) 2,933 159 220 12,30 9 67,115 1,653 306 335 DADRA & NAGAR HAVELI (26) 2,588 220 181 19,95 0 54,455 3,247 451 957 MAHARAS HTRA (27) 2,49,129 30,50 9 33,678 18,31, 160 25,37,638 1,01, 924 87,034 69,11 1 ANDHRA PRADESH (28) 49,670 7,898 10,847 5,33,5 44 2,31,471 37,07 9 13,104 24,79 0 KARNATA KA (29) 1,24,179 12,95 3 38,944 8,40,4 42 6,57,819 61,44 4 63,643 31,55 7 GOA (30) 8,838 1,149 953 45,85 4 64,852 6,212 1,716 1,661 LAKSHAD WEEP (31) 59 7 234 118 2,200 19 340 29 KERALA (32) 24,874 1,219 3,195 1,02,2 55 1,29,875 6,970 6,758 19,70 9 TAMIL NADU (33) 43,823 3,271 20,435 3,73,2 92 2,19,262 14,18 1 38,727 21,73 2 PUDUCHE RRY (34) 7,389 925 2,014 1,03,4 34 43,572 2,566 2,908 16,10 7 ANDAMA N & NICOBAR ISLANDS (35) 1,419 107 226 16,73 1 26,304 1,915 455 340

Source: D3 Table, Census 2011.

3.a. From the following uniformly distributed data scene calculate the probability w.r.t statement.

The weekly output of a steel mill is a uniformly distributed random variable that lies between 110 and 175 metric tons.

1. Compute the probability that the steel mill will produce more than 150 metric tons next week.
2. Determine the probability that the steel mill will produce between 120 and 160 metric tons

3.b. Draw the histogram separately (for Person, male and female) and write the interpretation.

The following table shows the age group-wise total number of Migrants as per census 2011.

 Age Group Total number of Migrant persons Total number of Migrant Males Total number of Migrant Females 0-4 1,89,62,713 98,34,738 91,27,975 5-9 2,09,17,565 1,09,59,506 99,58,059 10-14 2,38,76,335 1,24,25,108 1,14,51,227 15-19 2,92,02,399 1,26,83,733 1,65,18,666 20-24 4,68,55,749 1,31,97,283 3,36,58,466 25-29 5,05,67,231 1,30,45,214 3,75,22,017 30-34 4,64,20,105 1,21,34,009 3,42,86,096 35-39 4,51,14,917 1,20,60,030 3,30,54,887 40-44 3,81,61,379 1,09,00,143 2,72,61,236 45-49 3,31,51,742 97,04,026 2,34,47,716 50-54 2,57,83,138 79,40,152 1,78,42,986 55-59 2,13,54,664 61,61,754 1,51,92,910 60-64 1,97,49,108 54,01,736 1,43,47,372 65-69 1,38,28,278 36,87,082 1,01,41,196 70-74 96,96,149 26,62,421 70,33,728 75-79 48,34,573 13,41,572 34,93,001 80+ 57,14,991 14,61,296 42,53,695

Source: D4 table, census 2011

Note: Here, students may use Excel for the preparation of the Histogram.

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