The distribution of course grades in a very large class is (approximately) Normal with mean 48 and standard deviation 14. The minimum possible grade is 0 and the maximum possible grade is 120. A grade of 60 or more is required to pass the course. The course instructor is considering the possibility of a "bell curve" that will increase the mean grade to 77 and decrease the standard deviation to 6. Suppose the instructor will toss a fair or balanced coin to decide what to do and will use the bell curve only if the coin comes up heads. What is the probability that the student at the 50-th percentile will pass the course?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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N
<-3.4
3.3
<<-3.2
<-3.1
-3.0
-2.9
2.8
-2.7
-2.6
2.5
<-2.4
<-2.3
-2.2
<-2.1
<-2.0
1.9
1.8
1.7
1.6
1.5
<-1.4
-1.3
-1.2
-1.1
1.0
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
-0.0
.00
.0003
.0005
.0007
.0010
.0013
.0019
.0026
.0035
.0047
.0062
.0082
.0107
.0139
.0179
.0228
0287
.0359
.0446
0548
.0668
.0808
.0968
1151
1357
1587
.1841
2119
.2420
.2743
.3085
.3446
.3821
4207
.4602
.5000
.01
.0003
.0005
.0007
.0009
.0013
.0018
.0025
.0034
.0045
.0060
.0080
.0104
.0136
.0174
.0222
.0281
.0351
.0436
.0537
.0655
.0793
.0951
.1131
.1335
.1562
.1814
.2090
.2389
.2709
.3050
.3409
.3783
.4168
4562
.4960
.02
.0003
.0005
.0006
.0009
.0013
.0018
.0024
.0033
.0044
.0059
.0078
.0102
0132
.0170
.0217
.0274
.0344
.0427
0526
.0643
.0778
.0934
.1112
.1314
.1539
.1788
2061
.2358
.2676
.3015
3372
3745
4129
.4522
.4920
.03
.0003
.0004
.0006
.0009
.0012
.0017
.0023
.0032
.0043
.0057
.0075
.0099
0129
.0166
0212
.0268
.0336
.0418
.0516
.0630
.0764
.0918
.1093
.1292
.1515
.1762
2033
2327
.2643
2981
3336
.3707
4090
4483
.4880
.04
.0003
.0004
.0006
.0008
.0012
.0016
.0023
.0031
.0041
.0055
.0073
.0096
.0125
.0162
0207
.0262
.0329
.0409
.0505
.0618
0749
.0901
.1075
.1271
1492
1736
.2005
.2296
.2611
2946
.3300
.3669
4052
.4443
.4840
.05
.0003
.0004
.0006
.0008
.0011
.0016
.0022
.0030
.0040
.0054
.0071
.0094
0122
.0158
.0202
.0256
.0322
.0401
€0495
.0606
.0735
.0885
.1056
1251
.1469
.1711
.1977
.2266
2578
.2912
.3264
.3632
4013
.4404
.4801
.06
.0003
.0004
.0006
.0008
.0011
.0015
.0021
.0029
.0039
.0052
.0069
.0091
0119
.0154
.0197
.0250
.0314
.0392
.0485
0594
0721
0869
.1038
.1230
.1446
168
.1949
.2236
.2546
2877
3228
.3594
3974
.4364
.4761
.07
.0003
.0004
.0005
.0008
.0011
.0015
.0021
.0028
.0038
.0051
.0068
.0089
.0116
.0150
.0192
0244
.0307
.0384
.0475
.0582
.0708
0853
.1020
.1210
.1423
.1660
.1922
.2206
2514
2843
.3192
.3557
3936
.4325
.4721
.08
.0003
.0004
.0005
.0007
.0010
.0014
.0020
.0027
.0037
.0049
.0066
.0087
0113
.0146
.0188
.0239
.0301
.0375
.0465
.0571
0694
.0838
.1003
.1190
.1401
.1635
.1894
2177
2483
2810
.3156
.3520
3897
.4286
4681
.09
.0002
.0003
.0005
.0007
.0010
.0014
.0019
.0026
.0036
.0048
.0064
.0084
0110
.0143
.0183
0233
0294
.0367
.0455
.0559
.0681
.0823
.0985
1170
1379
1611
1867
.2148
.2451
.2776
.3121
.3483
.3859
4247
4641
Transcribed Image Text:N <-3.4 3.3 <<-3.2 <-3.1 -3.0 -2.9 2.8 -2.7 -2.6 2.5 <-2.4 <-2.3 -2.2 <-2.1 <-2.0 1.9 1.8 1.7 1.6 1.5 <-1.4 -1.3 -1.2 -1.1 1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 -0.0 .00 .0003 .0005 .0007 .0010 .0013 .0019 .0026 .0035 .0047 .0062 .0082 .0107 .0139 .0179 .0228 0287 .0359 .0446 0548 .0668 .0808 .0968 1151 1357 1587 .1841 2119 .2420 .2743 .3085 .3446 .3821 4207 .4602 .5000 .01 .0003 .0005 .0007 .0009 .0013 .0018 .0025 .0034 .0045 .0060 .0080 .0104 .0136 .0174 .0222 .0281 .0351 .0436 .0537 .0655 .0793 .0951 .1131 .1335 .1562 .1814 .2090 .2389 .2709 .3050 .3409 .3783 .4168 4562 .4960 .02 .0003 .0005 .0006 .0009 .0013 .0018 .0024 .0033 .0044 .0059 .0078 .0102 0132 .0170 .0217 .0274 .0344 .0427 0526 .0643 .0778 .0934 .1112 .1314 .1539 .1788 2061 .2358 .2676 .3015 3372 3745 4129 .4522 .4920 .03 .0003 .0004 .0006 .0009 .0012 .0017 .0023 .0032 .0043 .0057 .0075 .0099 0129 .0166 0212 .0268 .0336 .0418 .0516 .0630 .0764 .0918 .1093 .1292 .1515 .1762 2033 2327 .2643 2981 3336 .3707 4090 4483 .4880 .04 .0003 .0004 .0006 .0008 .0012 .0016 .0023 .0031 .0041 .0055 .0073 .0096 .0125 .0162 0207 .0262 .0329 .0409 .0505 .0618 0749 .0901 .1075 .1271 1492 1736 .2005 .2296 .2611 2946 .3300 .3669 4052 .4443 .4840 .05 .0003 .0004 .0006 .0008 .0011 .0016 .0022 .0030 .0040 .0054 .0071 .0094 0122 .0158 .0202 .0256 .0322 .0401 €0495 .0606 .0735 .0885 .1056 1251 .1469 .1711 .1977 .2266 2578 .2912 .3264 .3632 4013 .4404 .4801 .06 .0003 .0004 .0006 .0008 .0011 .0015 .0021 .0029 .0039 .0052 .0069 .0091 0119 .0154 .0197 .0250 .0314 .0392 .0485 0594 0721 0869 .1038 .1230 .1446 168 .1949 .2236 .2546 2877 3228 .3594 3974 .4364 .4761 .07 .0003 .0004 .0005 .0008 .0011 .0015 .0021 .0028 .0038 .0051 .0068 .0089 .0116 .0150 .0192 0244 .0307 .0384 .0475 .0582 .0708 0853 .1020 .1210 .1423 .1660 .1922 .2206 2514 2843 .3192 .3557 3936 .4325 .4721 .08 .0003 .0004 .0005 .0007 .0010 .0014 .0020 .0027 .0037 .0049 .0066 .0087 0113 .0146 .0188 .0239 .0301 .0375 .0465 .0571 0694 .0838 .1003 .1190 .1401 .1635 .1894 2177 2483 2810 .3156 .3520 3897 .4286 4681 .09 .0002 .0003 .0005 .0007 .0010 .0014 .0019 .0026 .0036 .0048 .0064 .0084 0110 .0143 .0183 0233 0294 .0367 .0455 .0559 .0681 .0823 .0985 1170 1379 1611 1867 .2148 .2451 .2776 .3121 .3483 .3859 4247 4641
The distribution of course grades in a very large class is (approximately) Normal with mean 48 and standard deviation
14. The minimum possible grade is 0 and the maximum possible grade is 120. A grade of 60 or more is required to pass
the course. The course instructor is considering the possibility of a "bell curve" that will increase the mean grade to 77
and decrease the standard deviation to 6. Suppose the instructor will toss a fair or balanced coin to decide what to do
and will use the bell curve only if the coin comes up heads. What is the probability that the student at the 50-th
percentile will pass the course?
Transcribed Image Text:The distribution of course grades in a very large class is (approximately) Normal with mean 48 and standard deviation 14. The minimum possible grade is 0 and the maximum possible grade is 120. A grade of 60 or more is required to pass the course. The course instructor is considering the possibility of a "bell curve" that will increase the mean grade to 77 and decrease the standard deviation to 6. Suppose the instructor will toss a fair or balanced coin to decide what to do and will use the bell curve only if the coin comes up heads. What is the probability that the student at the 50-th percentile will pass the course?
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