a) Grace Floral Shop sells several types of roses for all occasions. It is known that 43% of the roses that is sold by Grace Floral Shop are Eden Roses. 12 roses are ordered to put in a bouquet (ii) Stating its parameter(s), what is the probability distribution of this variable?  (iii) State the conditions that influence your choice of distribution.  (iv) Calculate the probability that at most 2 of the roses were Eden Roses.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Question

a) Grace Floral Shop sells several types of roses for all occasions. It is known that 43% of the roses that is sold by Grace Floral Shop are Eden Roses. 12 roses are ordered to put in a bouquet

(ii) Stating its parameter(s), what is the probability distribution of this variable? 
(iii) State the conditions that influence your choice of distribution. 
(iv) Calculate the probability that at most 2 of the roses were Eden Roses.

Table 3
AREAS IN TAIL OF THE NORMAL DISTRIBUTION
The function tabulated is 1 - +(u) where (u) is the cumulative distribution function of a
standardised Normal variable u. Thus 1 - (u)= S e-u/2 du is the probability that a
v2n
standa rdised Normal variable selected at random will be greater
(-=)
1- (u)
than a value of u
(x - )
. 03
. 04
.00
.01
.02
.05
.06
.07
.08
09
. 5000
.4602
.4207
.3821
.3446
.4960
.4562
.4168
.3783
.3409
.4920
.4522
.4129
.3745
.3372
.4880
.4483
:4090
.3707
.3336
.4840
.4443
.4052
.3669
.3300
.4801
.4404
.4013
.3632
.3264
0.0
.4761
.4364
3974
.3594
3228
.4721
.4325
0.1
0.2
0.3
0.4
.3936
.3557
.3192
.4681
.4286
.3897
.3520
.3156
.4641
.4247
.3859
.3483
.3121
0.5
0.6
.3085
.2743
.2420
.2119
.3050
.2709
.2389
.2090
.3015
.2676
.2358
.2061
.1788
.2981
.2643
.2327
.2033
.2946
.2611
.2296
.2005
.1736
2912
.2578
.2266
.1977
.1711
.2877
.2546
.2236
.2843
.2514
.2206
.1922
.2810
.2483
.2177
.1894
.2776
.2451
.2148
. 1867
. 1611
0.7
0.8
.1949
.1685
0.9
.1841
.1814
.1762
.1660
.1635
. 1587
. 1357
.1151
. 0968
.0808
.1562
. 1335
.1131
.1539
.1314
.1515
.1292
.1093
.0918
.0764
.1446
. 1230
.1038
.0869
.0721
.1423
. 1210
.1020
1.0
.1492
. 1271
.1075
.0901
.1469
.1251
.1056
.1401
.1190
.1003
.0838
.0694
.1379
1.1
1.2
1.3
1.4
.1112
.0934
.0778
.1170
. 0985
.0823
.0681
.0951
.0793
.0853
.0708
.0885
.0749
.0735
1.5
1.6
1.7
1.8
1.9
.0668
.0548
.0446
.0359
.02 87
.0655
.0537
.0436
.0351
.02 81
.0643
.0526
.0427
.0344
. 0274
.0630
.0516
.0418
.0336
.0268
.0618
.0505
.0409
.0329
.0262
.0606
.0495.
.0401
.0322
. 0256
.0594
.0485
.0392
. 0314
.0250
.0582
.0475.
.0384
.0307
.0244
.0571
.0465
.0375
.0301
.0559
.0455
.0367
.0294
.0233
.0239
. 02275
.01786 .01743 .01700
.01390 .01355 .01321
.01072 .01044 .01017
.00820 - .00798 .00776
. 02222 .02169
2.0
2.1
2.2
2.3
02118
.01659
.01287
. 02068 . 02018 .01970 .01923
.01539 .01500
.01191
. 00939 . 00914
.00695
.01876 .01831
01463
.01618 .01578
.01255 .01222
. 00964
. 00734 .00714
.01160
.00889
.00676
.01426
.01130 .01101
00866 .00842
.00657
.00990
2.4
.00755
. 00639
. 00621
.00466
.00347
.00256
.00187
. 00523
2.5
2.6
2.7
2.8
.00604 .00587
.00440
.00336 .00326
. 00240
.00175
. 00508
.00379
.002 80
. 002 05
.00149
.00570
.00539
.00427 .00415 .00402 .00391
. 00307 .00298
.00226 .00219
.00164 . 00159
.00554
.00494
.00368 . 00357
.00272 .00264
.00199 .00193
.00144 .00139
.00480
00453
.002 89
.00212
.00154
.00317
.00248
.00181
.00233
.00169
2.9
3.0
.00135
.00097
.00069
3.1
3.2
3.3
3.4
.00048
.00034
3.5
3.6
3.7
.00023
. 00016
.00011
3.8
3.9
.00007
.00005
4.0
00003
Transcribed Image Text:Table 3 AREAS IN TAIL OF THE NORMAL DISTRIBUTION The function tabulated is 1 - +(u) where (u) is the cumulative distribution function of a standardised Normal variable u. Thus 1 - (u)= S e-u/2 du is the probability that a v2n standa rdised Normal variable selected at random will be greater (-=) 1- (u) than a value of u (x - ) . 03 . 04 .00 .01 .02 .05 .06 .07 .08 09 . 5000 .4602 .4207 .3821 .3446 .4960 .4562 .4168 .3783 .3409 .4920 .4522 .4129 .3745 .3372 .4880 .4483 :4090 .3707 .3336 .4840 .4443 .4052 .3669 .3300 .4801 .4404 .4013 .3632 .3264 0.0 .4761 .4364 3974 .3594 3228 .4721 .4325 0.1 0.2 0.3 0.4 .3936 .3557 .3192 .4681 .4286 .3897 .3520 .3156 .4641 .4247 .3859 .3483 .3121 0.5 0.6 .3085 .2743 .2420 .2119 .3050 .2709 .2389 .2090 .3015 .2676 .2358 .2061 .1788 .2981 .2643 .2327 .2033 .2946 .2611 .2296 .2005 .1736 2912 .2578 .2266 .1977 .1711 .2877 .2546 .2236 .2843 .2514 .2206 .1922 .2810 .2483 .2177 .1894 .2776 .2451 .2148 . 1867 . 1611 0.7 0.8 .1949 .1685 0.9 .1841 .1814 .1762 .1660 .1635 . 1587 . 1357 .1151 . 0968 .0808 .1562 . 1335 .1131 .1539 .1314 .1515 .1292 .1093 .0918 .0764 .1446 . 1230 .1038 .0869 .0721 .1423 . 1210 .1020 1.0 .1492 . 1271 .1075 .0901 .1469 .1251 .1056 .1401 .1190 .1003 .0838 .0694 .1379 1.1 1.2 1.3 1.4 .1112 .0934 .0778 .1170 . 0985 .0823 .0681 .0951 .0793 .0853 .0708 .0885 .0749 .0735 1.5 1.6 1.7 1.8 1.9 .0668 .0548 .0446 .0359 .02 87 .0655 .0537 .0436 .0351 .02 81 .0643 .0526 .0427 .0344 . 0274 .0630 .0516 .0418 .0336 .0268 .0618 .0505 .0409 .0329 .0262 .0606 .0495. .0401 .0322 . 0256 .0594 .0485 .0392 . 0314 .0250 .0582 .0475. .0384 .0307 .0244 .0571 .0465 .0375 .0301 .0559 .0455 .0367 .0294 .0233 .0239 . 02275 .01786 .01743 .01700 .01390 .01355 .01321 .01072 .01044 .01017 .00820 - .00798 .00776 . 02222 .02169 2.0 2.1 2.2 2.3 02118 .01659 .01287 . 02068 . 02018 .01970 .01923 .01539 .01500 .01191 . 00939 . 00914 .00695 .01876 .01831 01463 .01618 .01578 .01255 .01222 . 00964 . 00734 .00714 .01160 .00889 .00676 .01426 .01130 .01101 00866 .00842 .00657 .00990 2.4 .00755 . 00639 . 00621 .00466 .00347 .00256 .00187 . 00523 2.5 2.6 2.7 2.8 .00604 .00587 .00440 .00336 .00326 . 00240 .00175 . 00508 .00379 .002 80 . 002 05 .00149 .00570 .00539 .00427 .00415 .00402 .00391 . 00307 .00298 .00226 .00219 .00164 . 00159 .00554 .00494 .00368 . 00357 .00272 .00264 .00199 .00193 .00144 .00139 .00480 00453 .002 89 .00212 .00154 .00317 .00248 .00181 .00233 .00169 2.9 3.0 .00135 .00097 .00069 3.1 3.2 3.3 3.4 .00048 .00034 3.5 3.6 3.7 .00023 . 00016 .00011 3.8 3.9 .00007 .00005 4.0 00003
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