The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of 19 minutes and a standard deviation of 2.5 minutes. (a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take longer, the customer will receive the service for half-price. What percent of customers receive the service for half-price? (b) If the automotive center does not want to give the discount to more than 4% of its customers, how long should it make the guaranteed time limit?
The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of 19 minutes and a standard deviation of 2.5 minutes. (a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take longer, the customer will receive the service for half-price. What percent of customers receive the service for half-price? (b) If the automotive center does not want to give the discount to more than 4% of its customers, how long should it make the guaranteed time limit?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
100%
The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of 19 minutes and a standard deviation of 2.5 minutes.
(a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take longer, the customer will receive the service for half-price. What percent of customers receive the service for half-price?
(b) If the automotive center does not want to give the discount to more than 4% of its customers, how long should it make the guaranteed time limit?
Click here to view the standard normal distribution table (page 1).
Click here to view the standard normal distribution table (page 2).
Transcribed Image Text:7/8/22, 2:37 PM
८
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
N
Area
0.00
0.5000
0.5398 0.5438
0.5793 0.5832
0.6179
0.6554
0.6915
0.7257
0.7580
0.7881
0.8159
0.8413
0.8643
0.8849
0.9032
0.9192
0.9641
0.9713
0.9772
0.9821
0.9861
0.9893
0.9918
0.9938
0.9953
0.9965
0.9974
0.9981
0.9987
0.9990
0.9993
0.01
0.02
0.5040 0.5080
0.5120
0.5160
0.5517
0.5557
0.5478
0.5871 0.5910 0.5948
0.6217 0.6255 0.6293 0.6331
0.6591
0.9995
0.9997
0.00
0.9332
0.9345
0.9357
0.9452 0.9463 0.9474
0.9554 0.9564 0.9573
0.6950
0.7019
0.6985
0.7054
0.7291 0.7324 0.7357 0.7389
0.7611
0.7642
0.7673 0.7704
0.7910
0.7939
0.8186
0.8212
0.8438 0.8461
0.8665
0.8869
0.9049
0.9207
0.6628 0.6664 0.6700 0.6736
0.9940
0.9955
0.9966
0.9975
0.9982
0.9066
0.9222
Standard Normal Distribution
0.03
0.04
0.05
0.8485
0.8686 0.8708
0.8888
0.8907
0.9995
0.9997
0.01
0.7967
0.8238
0.9370
0.9382
0.9484
0.9495
0.9582 0.9591
0.9649 0.9656 0.9664 0.9671
0.9719
0.9726
0.9732
0.9738
0.9987 0.9987
0.9991
0.9991
0.9993
0.9994
0.9082
0.9236
0.9778 0.9783 0.9788 0.9793
0.9826 0.9830 0.9834 0.9838
0.9864 0.9868 0.9871 0.9875
0.9896 0.9898 0.9901 0.9904
0.9920
0.9922
0.9925
0.9927
0.9941
0.9943
0.9956
0.9957
0.9967 0.9968
0.9995
0.9997
0.02
0.9976 0.9977
0.9982
0.9983
0.7088
0.7422
0.7734
0.7995 0.8023
0.8264 0.8289
0.9996
0.9997
0.03
Standard Normal Distribution Table (page 2)
0.9945
0.9959
0.8508
0.8531
0.8729
0.8749 0.8770
0.8925
0.8944
0.8962
0.9099
0.9115
0.9251 0.9265
0.9969
0.9977
0.9984
0.9988 0.9988
0.9991
0.9992
0.9994
0.9994
0.06
0.07
0.5199
0.5239
0.5279
0.5596
0.5636 0.5675
0.5987
0.6026
0.6064
0.6368 0.6406
0.6443 0.6480
0.6772
0.6808 0.6844
0.9996
0.9997
0.04
0.7123
0.7454
0.7764
0.9946
0.9960
0.9970
0.9978
0.9984
0.9989
0.9992
0.9994
0.9996
0.9997
0.05
0.7157
0.7190
0.7486 0.7517
0.7794 0.7823
0.8051
0.8106
0.8078
0.8315 0.8340 0.8365
0.8554 0.8577
0.8790
0.8980
0.9394 0.9406 0.9418
0.9505 0.9515 0.9525
0.9599
0.9608 0.9616
0.9678 0.9686
0.9744 0.9750
0.9803
0.9842 0.9846
0.9878 0.9881
0.9906 0.9909
0.9798
0.9929 0.9931
0.9131
0.9147
0.9279 0.9292
0.9948
0.9961
0.9971
0.9979
0.9985
0.08
0.5319
0.5714
0.6103
0.9996
0.9997
0.06
0.8599
0.8810
0.8997
0.9162
0.9306
0.9693 0.9699
0.9756 0.9761
0.9808 0.9812
0.9850 0.9854
0.9884 0.9887
0.9911
0.9913
0.9932 0.9934
0.9996
0.9997
0.07
0.9949
0.9951
0.9962
0.9963
0.9972 0.9973
0.9979 0.9980
0.9985 0.9986
0.9989 0.9989 0.9990
0.9992
0.9992
0.9993
0.9994
0.9995
0.9995
0.9429
0.9441
0.9535
0.9545
0.9625 0.9633
0.09
0.5359
0.5753
0.6141
0.9996
0.9997
0.08
0.6517
0.6879
0.7224
0.7549
0.7852
0.8133
0.8389
0.8621
0.8830
0.90 15
0.9177
0.9319
0.9706
0.9767
0.9817
0.9857
0.9890
0.9916
0.9936
0.9952
0.9964
0.9974
0.9981
0.9986
0.9990
0.9993
0.9995
0.9997
0.9998
0.09
Transcribed Image Text:7/8/22, 2:37 PM
Area
N
-3.4
-3.3
-3.2
-3.1
-3.0
-29
-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
-1.0
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
-0.0
N
0.00
0.0003
0.0005
0.0007
0.0010
0.0013
0.01
0.0003
0.0005
0.0007
0.0009
0.0013
0.0019
0.0018
0.0026
0.0025
0.0035 0.0034 0.0033
0.0047
0.0062
0.02
0.0003
0.0005
0.0006
0.0179 0.0174
0.0228 0.0222
0.0009
0.0013
0.0082
0.0080
0.0078
0.0107
0.0104
0.0102
0.0139 0.0136 0.0132
0.00
0.2743 0.2709
0.3085 0.3050
0.0170
0.0217
Standard Normal Distribution
0.03
0.04
0.05
0.0003
0.0004
0.0006
0.0018 0.0017
0.0024 0.0023 0.0023
0.0032 0.0031
0.0045 0.0044 0.0043 0.0041
0.0055
0.0060
0.0059
0.0057
0.0003
0.0004
0.0006
0.0009 0.0008
0.0012
0.0166
0.0212
0.0075
0.0099 0.0096
0.0129
0.0125
Standard Normal Distribution Table (page 1)
0.0012
0.0016 0.0016 0.0015
0.0022
0.0030
0.0162
0.0207
0.06
0.0003
0.0003
0.0004
0.0004
0.0006 0.0006
0.0054 0.0052
0.0073 0.0071 0.0069
0.2327
0.2676 0.2643
0.3821
0.3015 0.2981
0.3446 0.3409 0.3372 0.3336 0.3300
0.3783 0.3745 0.3707 0.3669
0.4168 0.4129 0.4090 0.4052
0.4522 0.4483 0.4443
0.4207
0.4602
0.4562
0.5000
0.4960
0.4920
0.4880
0.4840
0.01
0.02
0.03
0.04
0.0008 0.0008 0.0008
0.0011 0.0011
0.0011
0.0015
0.0021 0.0021
0.0029 0.0028
0.0040 0.0039 0.0038
0.0287 0.0281 0.0274
0.0268
0.0262
0.0359 0.0351 0.0344
0.0336
0.0329
0.0668
0.0446 0.0436 0.0427 0.0418 0.0409
0.0548 0.0537
0.0526 0.0516
0.0655 0.0643 0.0630 0.0618
0.0808 0.0793 0.0778 0.0764 0.0749
0.0968 0.0951 0.0934 0.0918 0.0901
0.1151 0.1131 0.1112 0.1093
0.1357 0.1335 0.1314 0.1292 0.1271
0.1492
0.1587 0.1562
0.1814
0.1539 0.1515
0.1788 0.1762 0.1736
0.1841
0.1711 0.1685
0.2119
0.2090
0.2061
0.2033
0.2005
0.1977 0.1949
0.2420 0.2389
0.2358
0.2296
0.2266
0.2236
0.2611 0.2578
0.2546 0.2514
0.2946
0.2912
0.2877
0.0256
0.0322
0.0401
0.0505 0.0495
0.0606
0.0250
0.0314
0.0392
0.07
0.08
0.09
0.0003
0.0003
0.0002
0.0004 0.0004 0.0003
0.0005
0.0005
0.0005
0.0485
0.0594
0.0735 0.0721
0.0885 0.0869
0.1075 0.1056 0.1038
0.0068
0.0089
0.0094 0.0091
0.0122 0.0119 0.0116
0.0158
0.0150
0.0146
0.0154
0.0202 0.0197 0.0192 0.0188
0.1251 0.1230
0.1469 0.1446
0.0007
0.0010
0.0037
0.0051 0.0049
0.0014
0.0020
0.0027
0.0244
0.0307
0.0384
0.0475
0.0582
0.0066
0.0087
0.0113
0.0239
0.0301
0.0375
0.0465
0.0571
0.0708 0.0694
0.0853
0.0838
0.1020
0.1003
0.1210 0.1190
0.1423 0.1401
0.1660 0.1635
0.1922
0.1894
0.2206
0.2177
0.2483
0.2843 0.2810
0.3192 0.3156
0.3264 0.3228
0.3632 0.3594
0.3557 0.3520
0.4013 0.3974
0.3936
0.3897
0.4404 0.4364
0.4325
0.4801 0.4761 0.4721
0.05
0.06
0.07
0.4286
0.4681
0.08
0.0007
0.0010
0.0014
0.0019
0.0026
0.0036
0.0048
0.0064
0.0084
0.0110
0.0143
0.0183
0.0233
0.0294
0.0367
0.0455
0.0559
0.0681
0.0823
0.0985
0.1170
0.1379
0.1611
0.1867
0.2148
0.2451
0.2776
0.3121
0.3483
0.3859
0.4247
0.4641
0.09
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