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 90 or more is required to get "A+". 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. What is the proportion of students that will get "A+" if the bell curve is applied?
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 90 or more is required to get "A+". 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. What is the proportion of students that will get "A+" if the bell curve is applied?
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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Question
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 90 or more is required to get
"A+". 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. What is the proportion of students that will get "A+" if the bell curve is applied?
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
-1.3
-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
1685
.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
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