Praktikum Week 3
Hanif Syahrul Ramadhan_2404010004
2026-02-28
- Buat simulasi untuk distribusi diskrit dan distribusi kontinu. A. Distribusi Diskrit – Binomial Distribusi Binomial digunakan untuk memodelkan jumlah keberhasilan dari n percobaan Bernoulli dengan probabilitas sukses p. Misal: n = 10 (jumlah percobaan) p = 0.3 (probabilitas sukses) Simulasi sebanyak 1000 kali
set.seed(123)
n <- 10
p <- 0.3
sim_binom <- rbinom(1000, size = n, prob = p)
sim_binom## [1] 2 4 3 5 5 1 3 5 3 3 6 3 4 3 1 5 2 1 2 6 5 4 3 7 4 4 3 3 2 1 6 5 4 4 0 3 4
## [38] 2 2 2 1 3 3 2 2 1 2 3 2 5 1 3 4 1 3 2 1 4 5 2 4 1 3 2 4 3 4 4 4 3 4 3 4 0
## [75] 3 2 2 3 2 1 2 4 3 4 1 3 6 5 5 2 1 4 2 4 2 2 4 1 3 3 3 2 3 6 3 5 5 3 3 1 5
## [112] 2 1 5 4 1 3 6 3 3 3 2 2 2 2 6 2 1 1 4 3 5 4 4 3 4 4 4 6 3 2 3 0 2 4 2 2 1
## [149] 2 4 4 3 3 2 1 3 3 2 3 2 3 2 4 2 2 3 4 2 3 2 3 2 5 4 4 3 2 3 5 3 4 2 4 2 3
## [186] 3 2 3 5 5 2 2 6 3 5 3 3 4 2 3 2 6 3 3 3 5 2 2 2 2 3 2 2 4 1 4 2 3 4 5 2 6
## [223] 4 4 1 3 3 3 4 5 3 3 3 1 2 3 2 4 2 4 3 4 2 3 2 4 3 6 6 4 2 2 3 2 3 4 2 3 3
## [260] 5 5 5 4 5 3 3 2 2 0 3 5 0 1 2 4 4 6 3 1 3 4 1 3 2 1 3 1 2 1 4 2 1 1 5 4 4
## [297] 6 1 1 4 4 0 4 4 3 3 2 0 3 3 3 3 4 1 2 4 4 2 2 5 5 2 1 4 1 1 8 1 2 5 3 2 4
## [334] 4 2 3 4 3 3 6 3 1 3 2 3 2 6 3 2 3 1 6 3 2 3 6 4 3 2 4 1 2 5 2 2 4 2 0 3 3
## [371] 3 2 5 3 3 6 4 2 2 6 3 4 2 4 3 5 2 2 1 2 6 2 4 4 1 2 2 1 1 7 6 1 5 3 3 3 4
## [408] 1 2 4 2 4 2 3 2 2 5 2 3 0 3 3 3 2 5 3 2 3 2 5 6 3 2 7 2 3 1 3 1 2 2 3 4 2
## [445] 5 4 4 1 2 4 3 2 2 1 2 5 4 4 2 1 6 3 3 2 3 2 2 4 2 4 1 4 3 4 4 3 3 0 2 4 2
## [482] 4 2 4 5 1 1 4 3 4 6 1 3 4 1 7 2 1 4 4 2 2 2 1 2 2 3 3 5 2 3 1 5 3 4 2 3 4
## [519] 1 4 2 2 2 1 3 4 5 0 6 2 5 4 3 4 1 4 2 4 3 2 4 1 4 2 4 6 1 5 4 3 2 2 3 5 3
## [556] 3 4 3 3 0 1 5 4 2 4 4 3 4 3 5 3 5 3 3 5 4 3 0 3 3 5 4 5 2 5 2 2 4 6 3 3 1
## [593] 6 1 1 5 3 2 5 1 2 4 2 2 2 4 1 4 2 2 3 1 0 7 3 4 5 4 6 1 5 5 4 2 1 2 2 5 2
## [630] 2 4 4 3 4 1 2 6 4 4 3 3 4 5 3 1 3 4 1 2 3 4 5 3 3 4 5 5 1 3 2 4 4 1 4 2 1
## [667] 5 2 3 2 0 3 1 2 3 3 4 2 3 3 4 4 4 5 5 3 3 2 3 2 1 3 3 1 2 3 2 1 3 2 4 2 0
## [704] 5 2 3 3 2 2 3 3 3 4 4 3 3 0 0 7 1 3 4 4 5 3 4 4 3 4 0 3 5 3 5 2 2 4 6 2 0
## [741] 7 1 1 3 2 3 4 1 4 5 2 2 2 1 3 3 3 5 1 2 3 2 3 3 3 1 1 3 4 4 5 4 4 4 1 2 2
## [778] 3 3 4 2 4 0 4 4 3 2 0 2 5 5 3 2 3 4 3 1 2 2 2 3 2 1 1 2 6 3 3 4 4 1 4 2 5
## [815] 4 1 2 1 3 3 4 2 3 7 4 1 3 1 2 4 0 4 3 4 4 3 4 4 2 1 6 4 3 1 3 2 5 0 2 1 2
## [852] 4 7 4 3 3 5 1 1 5 3 1 3 3 3 2 2 1 3 3 1 2 4 3 5 4 0 4 5 3 1 5 4 1 4 5 3 2
## [889] 2 2 3 4 4 3 4 4 0 2 1 4 5 3 5 3 4 3 4 5 4 1 0 1 5 3 2 6 3 3 3 2 4 1 2 5 4
## [926] 4 2 3 1 4 5 2 4 3 6 2 3 5 5 0 6 3 3 3 1 2 3 2 3 2 3 2 6 1 2 6 3 1 3 3 3 3
## [963] 3 1 5 3 3 1 4 3 4 1 4 2 2 3 5 0 2 3 3 4 5 3 5 4 1 2 2 3 1 2 3 3 3 4 3 3 4
## [1000] 1# Statistik ringkas
mean(sim_binom)## [1] 2.989var(sim_binom)## [1] 2.114994# Visualisasi
hist(sim_binom, probability = TRUE,
main = "Simulasi Distribusi Binomial",
col = "lightblue")
# Tambahkan kurva teoritis
x <- 0:n
points(x, dbinom(x, n, p), col="red", pch=19)
Penjelasan : Perintah rbinom() digunakan untuk menghasilkan 1000 data acak dari distribusi Binomial dengan parameter n = 10 dan p = 0.3. Nilai rata-rata dan varians kemudian dihitung menggunakan mean() dan var() untuk dibandingkan dengan nilai teoritis (μ = np dan σ² = np(1−p)). Histogram dibuat untuk melihat bentuk distribusi hasil simulasi.
B. Distribusi Kontinu – Normal Distribusi Normal sering digunakan untuk memodelkan fenomena alam seperti tinggi badan, berat badan, dan nilai ujian. Misal: Mean = 75 SD = 8 Simulasi 1000 data
set.seed(123)
mu <- 75
sigma <- 8
sim_normal <- rnorm(1000, mean = mu, sd = sigma)
sim_normal## [1] 70.51619 73.15858 87.46967 75.56407 76.03430 88.72052 78.68733
## [8] 64.87951 69.50518 71.43470 84.79265 77.87851 78.20617 75.88546
## [15] 70.55327 89.29531 78.98280 59.26706 80.61085 71.21767 66.45741
## [22] 73.25620 66.79196 69.16887 69.99969 61.50645 81.70230 76.22698
## [29] 65.89490 85.03052 78.41171 72.63943 82.16101 82.02507 81.57265
## [36] 80.50912 79.43134 74.50471 72.55230 71.95623 69.44234 73.33666
## [43] 64.87683 92.35165 84.66370 66.01513 71.77692 71.26676 81.23972
## [50] 74.33305 77.02655 74.77163 74.65704 85.94882 73.19383 87.13176
## [57] 62.60998 79.67691 75.99083 76.72753 78.03712 70.98141 72.33434
## [64] 66.85140 66.42567 77.42823 78.58568 75.42403 82.37814 91.40068
## [71] 71.07175 56.52665 83.04591 69.32639 69.49593 83.20457 72.72182
## [78] 65.23426 76.45043 73.88887 75.04611 78.08224 72.03472 80.15501
## [85] 73.23611 77.65426 83.77471 78.48145 72.39255 84.19046 82.94803
## [92] 79.38718 76.90985 69.97675 85.88522 70.19792 92.49866 87.26089
## [99] 73.11440 66.78863 69.31675 77.05507 73.02646 72.21966 67.38705
## [106] 74.63978 68.72076 61.65646 71.95819 82.35197 70.39722 79.86371
## [113] 62.05694 74.55550 79.15526 77.40923 75.84541 69.87435 68.20237
## [120] 66.80697 75.94117 67.42020 71.07554 72.95126 89.75090 69.78440
## [127] 76.88309 75.62369 67.30515 74.42954 86.55641 78.61203 75.32986
## [134] 71.62003 58.57402 84.05070 63.31488 80.91958 90.27283 63.44885
## [141] 80.61427 72.90242 62.42285 62.88266 62.18771 70.75275 63.30596
## [148] 80.50333 91.80087 64.70376 81.30191 81.15234 77.65762 66.93299
## [155] 74.04438 72.75684 79.50392 72.02049 82.81579 72.00335 83.42169
## [162] 66.60658 64.91876 100.92832 71.66514 77.38582 80.09256 71.12975
## [169] 79.13490 77.95172 73.27696 75.52234 74.72746 92.02762 69.06931
## [176] 66.23203 75.30231 77.48385 78.49219 71.33308 66.49339 85.10548
## [183] 72.20280 68.07590 73.10976 73.42259 83.87936 75.67790 81.03243
## [190] 71.00566 76.71556 72.40251 75.75667 67.83709 64.51359 90.97771
## [197] 79.80567 64.98983 70.11067 65.51616 92.59048 85.49930 72.87884
## [204] 79.34555 71.68528 71.19002 68.69118 70.24306 88.20726 74.56777
## [211] 75.95396 76.94950 84.85981 70.87149 67.05994 88.40558 71.47069
## [218] 69.21547 65.10982 64.72227 70.40821 79.94389 83.87879 80.66071
## [225] 72.09074 75.47800 69.36323 69.26225 82.07720 66.87526 90.64235
## [232] 74.27744 76.71631 69.09178 70.40489 64.46387 73.53660 78.35186
## [239] 77.59443 68.74771 68.69102 70.98241 86.96849 65.90157 73.56759
## [246] 90.21889 74.19220 64.12127 69.68184 78.88368 71.99518 70.50499
## [253] 72.24866 75.72397 87.78807 74.29148 83.64640 80.04603 74.09088
## [260] 62.73678 70.83106 71.08104 75.37724 85.40159 93.34463 87.38065
## [267] 73.93479 60.94778 71.88976 75.71366 81.76010 82.70022 80.47448
## [274] 63.83781 81.79714 71.42754 76.39842 75.59641 78.42533 75.19740
## [281] 61.66020 80.89197 78.08821 72.87479 75.94516 76.07231 76.76816
## [288] 88.12677 73.24760 76.34452 84.34707 83.43345 84.16210 70.38026
## [295] 91.01986 75.53361 89.93481 64.19278 75.16787 84.99932 69.27806
## [302] 68.97849 67.49169 66.57989 71.50272 77.64943 58.88632 76.69584
## [309] 84.89340 91.30059 85.40941 81.05420 61.18616 70.18795 72.18363
## [316] 80.62819 74.15463 64.93081 88.47549 82.29113 76.89944 84.74487
## [323] 64.28981 80.28656 70.81670 80.46996 74.51342 80.06369 85.68414
## [330] 75.05832 83.14047 65.49253 69.22716 87.15374 78.01910 58.58222
## [337] 64.08770 73.39375 81.92624 74.18493 79.99350 82.67204 88.36844
## [344] 75.44813 74.58414 60.97410 75.79462 70.42520 67.20792 73.56075
## [351] 83.11955 59.05801 71.58177 75.93310 67.85434 77.67122 78.29144
## [358] 74.73571 55.27281 95.57167 73.35761 80.20955 77.19013 83.19739
## [365] 81.54128 73.32165 78.02534 67.43673 81.85538 71.31169 94.33419
## [372] 61.79161 71.28810 81.60304 79.08106 70.28415 67.02575 76.15581
## [379] 74.88554 60.67775 75.27641 76.52184 76.39781 66.55986 78.80907
## [386] 86.02856 78.64989 65.91529 71.51484 77.76883 69.82363 57.73883
## [393] 82.07401 68.36418 70.41152 87.03120 68.80684 81.76585 64.91454
## [400] 72.16366 74.41155 65.65079 69.92201 74.76927 80.36557 61.79563
## [407] 72.20197 81.05125 70.68953 76.81834 78.93783 77.14268 80.22606
## [414] 74.01833 71.69059 53.85481 74.25647 78.44228 79.28319 70.55777
## [421] 89.23602 77.29140 76.01053 85.17813 69.25227 71.39729 94.17962
## [428] 75.08903 88.06855 63.49195 73.47587 78.02739 77.40031 66.95491
## [435] 75.15407 66.38063 80.70163 83.67820 57.20010 84.88555 65.07164
## [442] 78.63815 80.27922 73.40088 69.83909 76.32257 78.51055 82.06642
## [449] 58.58130 61.90897 86.44322 83.37303 78.48231 80.72143 82.33740
## [456] 53.71262 83.88222 71.12010 76.84493 72.63874 81.97572 72.21222
## [463] 79.14803 71.87452 66.25770 84.68008 80.92720 88.79410 75.52123
## [470] 84.00002 90.80335 72.74814 64.41639 73.08519 73.28767 76.21344
## [477] 88.69844 72.39085 77.98404 73.17853 75.16361 77.51246 85.62572
## [484] 75.97055 80.70274 81.23088 82.31819 70.40484 88.01505 71.95235
## [491] 74.15373 86.23240 85.35267 66.28007 68.01543 64.13537 76.45478
## [498] 76.31873 77.91292 79.41726 70.18486 67.05041 83.21428 81.00849
## [505] 62.92667 74.23882 67.83242 58.43399 76.20096 74.36631 74.22105
## [512] 76.72922 82.05972 76.64478 70.06851 69.12161 73.94558 77.48014
## [519] 66.68256 73.52553 82.73814 74.13376 69.41263 72.79244 83.91719
## [526] 79.40035 84.89341 76.11278 78.28220 70.53234 79.84297 70.94933
## [533] 63.63548 76.02394 90.56681 81.40731 84.32203 77.87085 70.13154
## [540] 73.38207 72.81402 71.25040 80.63334 65.42109 81.93093 81.91322
## [547] 65.41102 80.11594 94.44181 70.54228 81.75923 68.74239 83.88569
## [554] 76.99860 88.21532 63.32823 74.58962 70.78460 73.42188 69.96337
## [561] 68.32925 79.62978 66.29935 86.87225 65.51035 75.80863 79.26391
## [568] 79.69388 72.58603 75.63602 82.69011 63.34827 68.74608 77.56322
## [575] 71.44174 85.96003 80.38603 75.57733 62.93794 75.20880 72.46867
## [582] 74.18123 65.54753 78.98926 66.68835 73.19022 78.05141 68.73187
## [589] 79.66393 64.46792 52.52180 78.71974 81.72432 72.71324 79.03301
## [596] 65.75267 73.98281 59.46785 84.44945 89.87929 83.59210 74.78122
## [603] 74.73336 62.87146 81.32308 73.31413 69.74606 63.70379 72.60190
## [610] 68.20751 71.82376 65.25920 88.50072 74.87198 83.59956 54.18640
## [617] 71.37442 69.59614 65.21659 87.37287 63.67774 77.54712 81.77149
## [624] 76.42552 67.99796 82.52933 76.36470 66.49202 63.89561 91.69374
## [631] 69.57197 60.15543 79.26607 77.48184 64.16933 59.45635 74.06958
## [638] 84.11517 80.08899 71.05650 68.32649 77.16853 76.25883 80.03769
## [645] 71.83362 82.19483 68.35351 72.35564 80.92652 82.91977 59.49196
## [652] 75.85752 79.87023 63.39341 78.84500 68.37461 83.16202 79.30786
## [659] 81.15242 75.96575 81.90919 86.04412 90.72998 74.77284 57.00759
## [666] 75.25221 76.64449 73.75724 79.54631 83.08542 70.85614 72.64724
## [673] 78.18274 70.59821 75.73014 59.30634 66.04080 64.37796 68.17101
## [680] 69.45356 78.05844 82.85690 69.18093 67.02529 66.66649 71.68329
## [687] 73.08777 78.86894 72.42940 58.37209 74.26853 84.49749 84.53281
## [694] 68.68829 62.61779 94.66448 73.70062 74.22039 78.36459 62.08768
## [701] 69.17425 62.67646 69.45524 75.95080 64.08232 79.71986 77.31475
## [708] 67.76628 76.81060 80.98465 83.48876 73.29721 74.25091 74.30629
## [715] 86.53169 84.00058 81.67521 72.70127 77.98593 78.22632 66.66661
## [722] 61.17356 80.13464 62.76552 75.01347 77.00198 79.51094 76.51541
## [729] 69.13717 82.89093 88.90907 82.04943 59.45079 86.19661 74.55155
## [736] 79.19931 79.97627 74.22651 74.39789 83.15326 80.69282 82.92210
## [743] 94.06341 80.31533 76.65905 57.31494 96.53371 71.13859 93.99788
## [750] 77.99715 87.30744 74.12232 79.09177 76.71166 73.51103 74.03685
## [757] 83.10267 73.38833 58.69854 73.43289 79.31832 79.93165 79.93254
## [764] 61.46319 77.94994 82.74287 85.21263 73.20031 72.42486 86.90270
## [771] 61.65658 71.50536 78.65970 62.05781 77.23702 90.02291 74.96751
## [778] 72.77237 78.79929 72.76742 81.50720 82.23548 75.02153 65.58646
## [785] 64.45423 70.25602 81.37904 59.33436 59.90940 69.76976 78.15516
## [792] 67.69147 82.09399 77.66696 73.63488 81.55063 78.10692 71.43252
## [799] 76.84892 80.18011 77.85027 69.73592 81.84162 84.22349 77.21020
## [806] 76.15284 74.39500 92.29133 77.21052 73.73365 54.93666 62.47775
## [813] 74.37861 76.65035 77.21498 81.57205 73.44678 84.71671 67.62787
## [820] 65.33246 65.16811 80.93838 74.33664 81.31854 72.85835 70.26486
## [827] 72.05318 60.17907 65.64308 63.46372 83.43458 70.22136 81.31568
## [834] 87.13192 73.46580 77.27103 60.99146 68.45064 75.44972 77.39270
## [841] 68.92482 96.47887 71.33288 75.51395 80.19833 74.79185 69.85146
## [848] 83.36245 87.92436 74.76245 79.49814 74.22070 83.13164 65.75066
## [855] 93.56688 70.17175 63.32920 72.19266 76.17367 87.98897 82.28968
## [862] 76.13967 63.88413 68.07170 73.69372 95.42421 60.11818 84.04844
## [869] 70.78213 88.32793 65.88639 76.14899 66.20359 82.22813 86.87024
## [876] 90.60577 81.38081 89.74613 84.97139 73.94500 78.81630 67.22405
## [883] 73.51838 84.76771 79.33027 78.65886 66.69495 70.16389 68.88315
## [890] 78.16237 67.07594 79.49633 66.06867 89.62824 78.68473 69.39197
## [897] 76.92837 72.18037 77.96918 76.94826 66.88709 68.66949 77.39675
## [904] 88.11242 83.67694 70.00346 81.60738 74.61145 77.41051 77.08289
## [911] 95.60360 65.51769 75.80736 60.76018 79.71869 83.77287 86.56530
## [918] 59.59884 78.30216 87.74696 71.68787 73.30280 74.70770 77.92015
## [925] 80.32128 85.54257 74.23610 76.57022 94.90398 78.44879 76.51002
## [932] 64.26205 75.02285 73.22939 74.91163 70.39666 69.50547 69.23381
## [939] 73.28396 85.94506 83.39269 72.12020 61.51267 68.24333 71.33792
## [946] 75.82910 69.69914 91.05345 72.82186 65.28844 73.86991 66.95698
## [953] 76.24925 76.86907 77.84470 62.02513 76.76569 77.48360 63.63113
## [960] 82.64293 81.27337 93.39695 76.25362 75.37387 75.77269 75.55813
## [967] 60.21222 61.63098 74.37969 70.35146 75.43789 58.11033 63.01041
## [974] 66.18813 82.88847 66.21208 68.60389 75.63899 72.41803 76.17134
## [981] 93.44050 66.00317 72.55624 70.86592 87.09916 68.84412 74.34330
## [988] 81.29707 66.53128 88.24141 80.40610 66.40635 78.63662 73.29354
## [995] 77.50583 74.28020 83.56413 64.19120 70.81907 73.00647# Statistik ringkas
mean(sim_normal)## [1] 75.12902sd(sim_normal)## [1] 7.93356# Visualisasi
hist(sim_normal, probability = TRUE,
main = "Simulasi Distribusi Normal",
col = "lightgreen")
curve(dnorm(x, mean = mu, sd = sigma),
col = "red", add = TRUE)
Penjelasan : Perintah rnorm() menghasilkan 1000 data acak dari distribusi Normal dengan rata-rata 75 dan standar deviasi 8. Histogram menunjukkan bahwa data membentuk kurva lonceng (bell-shaped curve). Fungsi curve(dnorm()) menambahkan kurva distribusi normal teoritis untuk membandingkan hasil simulasi dengan teori.
- Buat studi kasus sendiri yang melibatkan simulasi variabel random dari distribusi yang telah dipelajari.
A. Studi Kasus: Simulasi Kelulusan Ujian Deskripsi Kasus Sebuah sekolah memiliki sistem ujian dengan ketentuan: - Setiap siswa memiliki probabilitas lulus 0.8 - Dalam satu kelas terdapat 30 siswa - Ingin diketahui distribusi jumlah siswa yang lulus jika disimulasikan 1000 kali Karena setiap siswa hanya memiliki dua kemungkinan (lulus/tidak), maka digunakan Distribusi Binomial.
set.seed(321)
n_siswa <- 30
p_lulus <- 0.8
sim_kelulusan <- rbinom(1000, size = n_siswa, prob = p_lulus)
sim_kelulusan## [1] 20 21 26 26 25 25 24 25 24 22 24 25 22 27 24 26 23 25 25 23 23 19 21 24
## [25] 24 23 18 24 26 24 26 23 23 18 23 24 23 28 23 24 22 25 24 22 22 25 26 21
## [49] 26 26 24 25 29 27 23 23 26 25 25 23 27 27 23 27 23 27 21 21 24 27 24 25
## [73] 28 21 20 22 24 21 24 26 27 26 24 19 24 25 24 22 22 23 23 26 24 20 22 24
## [97] 21 21 26 24 26 27 26 18 25 20 23 23 26 25 26 25 23 24 23 23 20 25 24 28
## [121] 21 26 24 23 21 24 26 24 21 24 29 26 25 23 24 21 23 27 27 26 26 26 25 24
## [145] 24 22 23 25 23 26 24 23 23 24 21 26 23 23 24 26 26 22 23 21 24 23 25 26
## [169] 21 24 27 24 28 22 26 23 24 23 24 24 27 25 25 24 22 24 27 25 26 24 19 25
## [193] 23 22 23 25 24 24 26 21 27 29 26 24 21 20 22 25 27 24 24 22 22 24 23 26
## [217] 25 26 25 25 27 26 23 23 24 26 23 23 21 20 23 23 25 21 24 21 26 25 25 21
## [241] 22 25 26 24 26 22 26 27 23 27 22 23 24 25 21 26 24 20 25 25 24 25 20 25
## [265] 22 26 24 23 22 22 20 24 25 26 25 22 25 18 24 26 25 23 23 29 26 28 24 17
## [289] 22 24 23 19 29 23 20 21 19 24 26 27 25 26 22 24 25 22 24 24 23 20 26 23
## [313] 25 28 24 26 23 23 21 25 24 27 23 25 24 22 21 25 26 24 26 22 24 24 24 20
## [337] 26 26 25 27 26 24 25 26 27 22 26 25 23 25 28 26 25 26 23 28 22 25 23 26
## [361] 22 28 22 25 20 23 26 26 28 19 24 26 25 23 25 24 25 25 24 23 25 26 25 21
## [385] 27 25 24 21 24 24 24 25 26 26 23 25 22 25 27 22 27 23 19 25 23 20 24 27
## [409] 26 26 23 26 22 24 26 23 25 25 23 22 26 27 27 22 25 21 21 21 24 23 21 25
## [433] 23 23 21 22 22 20 25 24 24 22 23 26 26 27 27 26 24 26 25 30 18 22 21 21
## [457] 24 23 20 26 24 25 22 27 21 25 25 27 23 24 25 23 25 24 22 26 27 23 24 24
## [481] 21 22 23 22 26 25 25 24 19 21 24 22 17 25 25 23 26 26 22 27 24 25 22 26
## [505] 26 23 27 26 23 23 26 20 23 24 26 25 21 26 25 23 18 22 25 24 22 25 25 27
## [529] 25 23 24 20 21 26 26 22 23 24 20 25 25 27 25 28 28 22 26 23 24 25 20 25
## [553] 23 27 26 26 24 25 27 22 23 24 24 22 25 27 19 23 23 25 27 22 26 26 23 22
## [577] 21 23 21 28 26 27 27 26 26 25 21 25 19 22 26 23 20 24 29 23 23 22 24 26
## [601] 26 23 28 23 28 20 19 27 25 22 26 25 23 25 22 25 23 23 23 23 22 26 22 26
## [625] 25 27 24 26 25 24 24 26 27 26 25 23 21 20 20 26 24 24 27 16 23 24 27 20
## [649] 25 23 25 24 26 24 21 23 24 21 26 26 25 23 25 25 27 24 24 26 22 24 23 27
## [673] 25 25 23 20 24 24 22 22 23 25 21 25 28 21 24 24 25 28 23 21 25 24 24 27
## [697] 23 24 25 23 21 22 25 24 25 27 23 29 25 26 22 28 22 26 25 25 21 24 27 29
## [721] 20 24 24 22 28 26 26 25 25 24 17 29 23 19 27 23 21 23 23 18 24 26 24 26
## [745] 27 21 18 22 23 22 22 24 26 19 23 27 26 23 21 26 22 22 24 26 22 23 25 27
## [769] 25 25 26 22 26 24 23 22 22 23 27 22 25 26 22 22 22 26 20 22 25 20 23 26
## [793] 27 22 22 26 21 22 24 23 25 20 23 23 24 22 27 25 26 22 25 24 26 23 23 21
## [817] 24 21 19 25 22 25 26 21 25 23 21 25 20 22 25 23 21 21 23 24 25 21 27 24
## [841] 23 22 25 24 22 22 21 22 22 25 26 22 20 23 23 22 21 25 24 21 21 24 24 23
## [865] 21 26 25 21 27 25 24 25 27 26 25 23 24 24 27 27 24 22 23 26 26 25 20 24
## [889] 23 28 22 20 26 25 26 25 20 21 24 23 23 21 25 24 23 26 23 23 26 24 25 23
## [913] 26 22 25 24 26 25 23 23 23 27 24 24 27 25 23 23 21 22 23 24 24 23 23 27
## [937] 23 23 20 19 25 24 20 26 23 23 23 20 24 22 26 25 22 24 26 26 25 22 21 25
## [961] 23 26 21 27 25 23 25 26 25 21 25 22 27 26 22 20 24 27 23 23 24 23 24 20
## [985] 27 28 22 25 27 27 22 24 25 27 26 27 22 23 26 26# Rata-rata jumlah siswa lulus
mean(sim_kelulusan)## [1] 23.906# Probabilitas minimal 25 siswa lulus
mean(sim_kelulusan >= 25)## [1] 0.421# Visualisasi
hist(sim_kelulusan, probability = TRUE,
main = "Simulasi Jumlah Siswa Lulus",
col = "orange")
x <- 0:n_siswa
points(x, dbinom(x, n_siswa, p_lulus), col="blue", pch=19)
Penjelasan : Hasil mean(sim_kelulusan) mendekati nilai teoritis μ = np = 30 × 0.8 = 24 siswa. Probabilitas minimal 25 siswa lulus dihitung menggunakan proporsi hasil simulasi yang memenuhi kondisi tersebut. Distribusi hasil simulasi akan cenderung simetris karena nilai p cukup besar (0.8), dan mendekati distribusi normal karena n cukup besar (prinsip Central Limit Theorem).