Standard Normal Distribution Table b. Determine the recovery time associated with the: (i) 16% of patients with the fastest recovery times x=_______days Round to 1 decimal place. (ii) 2% of patients with the slowest recovery times x=_____days Round to 1 decimal place.
Standard Normal Distribution Table b. Determine the recovery time associated with the: (i) 16% of patients with the fastest recovery times x=_______days Round to 1 decimal place. (ii) 2% of patients with the slowest recovery times x=_____days Round to 1 decimal place.
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
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Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Question
After surgery to replace an arthritic hip joint, the short-term recovery times until the patient is able to walk without assistance or pain are normally distributed , with a mean of 35.5 days and a standard deviation of 5.6 days.
Standard Normal Distribution Table
Standard Normal Distribution Table
b. Determine the recovery time associated with the:
(i) 16% of patients with the fastest recovery times
x=_______days
(ii) 2% of patients with the slowest recovery times
x=_____days
(iii) Middle 94% of short-term recovery times
(i) 16% of patients with the fastest recovery times
x=_______days
Round to 1 decimal place.
(ii) 2% of patients with the slowest recovery times
x=_____days
Round to 1 decimal place.
(iii) Middle 94% of short-term recovery times
_____days< x <_____days
Round to 1 decimal place.
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0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.0
0.5000
0.5040
0.5080
0.5120
0.5160
0.5199
0.5239
0.5279
0.5319
0.5359
0.1
0.5398
0.5438
0.5478
0.5517
0.5557
0.5596
0.5636
0.5675
0.5714
0.5753
0.2
0.5793
0.5832
0.5871
0.5910
0.5948
0.5987
0.6026
0.6064
0.6103
0.6141
L Open in Acrobat
0.3
0.6179
0.6217
0.6255
0.6293
0.6331
0.6368
0.6406
0.6443
0.6480
0.6517
0.4
0.6554
0.6591
0.6628
0.6664
0.6700
0.6736
0.6772
0.6808
0.6844
0.6879
0.5
0.6915
0.6950
0.6985
0.7019
0.7054
0.7088
0.7123
0.7157
0.7190
0.7224
0.6
0.7257
0.7291
0.7324
0.7357
0.7389
0.7422
0.7454
0.7486
0.7517
0.7549
The highlighted
value shows the area
0.7
0.7580
0.7611
0.7642
0.7673
0.7704
0.7734
0.7764
0.7794
0.7823
0.7852
under the standard
0.8
0.7881
0.7910
0.7939
0.7967
0.7995
0.8023
0.8051
0.8078
0.8106
0.8133
1
normal distribution
0.9
0.8159
0.8186
0.8212
0.8238
0.8264
0.8289
0.8315
0.8340
0.8365
0.8389
below z-score 0.90.
1.0
0.8413
0.8438
0.8461
0.8485
0.8508
0.8531
0.8554
0.8577
0.8599
0.8621
1.1
0.8643
0.8665
0.8686
0.8708
0.8729
0.8749
0.8770
0.8790
0.8810
0.8830
1.2
0.8849
0.8869
0.8888
0.8907
0.8925
0.8944
0.8962
0.8980
0.8997
0.9015
1.3
0.9032
0.9049
0.9066
0.9082
0.9099
0.9115
0.9131
0.9147
0.9162
0.9177
1.4
0.9192
0.9207
0.9222
0.9236
0.9251
0.9265
0.9279
0.9292
0.9306
0.9319
1.5
0.9332
0.9345
0.9357
0.9370
0.9382
0.9394
0.9406
0.9418
0.9429
0.9441
1.6
0.9452
0.9463
0.9474
0.9484
0.9495
0.9505
0.9515
0.9525
0.9535
0.9545
1.7
0.9554
0.9564
0.9573
0.9582
0.9591
0.9599
0.9608
0.9616
0.9625
0.9633
1.8
0.9641
0.9649
0.9656
0.9664
0.9671
0.9678
0.9686
0.9693
0.9699
0.9706
2
1.9
0.9713
0.9719
0.9726
0.9732
0.9738
0.9744
0.9750
0.9756
0.9761
0.9767
2.0
0.9772
0.9778
0.9783
0.9788
0.9793
0.9798
0.9803
0.9808
0.9812
0.9817
2.1
0.9821
0.9826
0.9830
0.9834
0.9838
0.9842
0.9846
0.9850
0.9854
0.9857
2.2
0.9861
0.9864
0.9868
0.9871
0.9875
0.9878
0.9881
0.9884
0.9887
0.9890
2.3
0.9893
0.9896
0.9898
0.9901
0.9904
0.9906
0.9909
0.9911
0.9913
0.9916
2.4
0.9918
0.9920
0.9922
0.9925
0.9927
0.9929
0.9931
0.9932
0.9934
0.9936
2.5
0.9938
0.9940
0.9941
0.9943
0.9945
0.9946
0.9948
0.9949
0.9951
0.9952
2.6
0.9953
0.9955
0.9956
0.9957
0.9959
0.9960
0.9961
0.9962
0.9963
0.9964
2.7
0.9965
0.9966
0.9967
0.9968
0.9969
0.9970
0.9971
0.9972
0.9973
0.9974
2.8
0.9974
0.9975
0.9976
0.9977
0.9977
0.9978
0.9979
0.9979
0.9980
0.9981
2.9
0.9981
0.9982
0.9982
0.9983
0.9984
0.9984
0.9985
0.9985
0.9986
0.9986
3.0
0.9987
0.9987
0.9987
0.9988
0.9988
0.9989
0.9989
0.9989
0.9990
0.9990
3.1
0.9990
0.9991
0.9991
0.9991
0.9992
0.9992
0.9992
0.9992
0.9993
0.9993
3.2
0.9993
0.9993
0.9994
0.9994
0.9994
0.9994
0.9994
0.9995
0.9995
0.9995
3.3
0.9995
0.9995
0.9995
0.9996
0.9996
0.9996
0.9996
0.9996
0.9996
0.9997
3.4
0.9997
0.9997
0.9997
0.9997
0.9997
0.9997
0.9997
0.9997
0.9997
0.9998
3.5
0.9998
0.9998
0.9998
0.9998
0.9998
0.9998
0.9998
0.9998
0.9998
0.9998
3.6
0.9998
0.9998
0.9999
0.9999
0.9999
0.9999
0.9999
0.9999
0.9999
0.9999
Note: For z 2 3.70, use P(Z< z) z 1.0000
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402 and 403.
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0.00
-3.6
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0002
0.0002
-3.5
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
L Open in Acrobat
-3.4
0.0002
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
-3.3
0.0003
0.0004
0.0004
0.0004
0.0004
0.0004
0.0004
0.0005
0.0005
0.0005
-3.2
0.0005
0.0005
0.0005
0.0006
0.0006
0.0006
0.0006
0.0006
0.0007
0.0007
-3.1
0.0007
0.0007
0.0008
0.0008
0.0008
0.0008
0.0009
0.0009
0.0009
0.0010
-3.0
0.0010
0.0010
0.0011
0.0011
0.0011
0.0012
0.0012
0.0013
0.0013
0.0013
-2.9
0.0014
0.0014
0.0015
0.0015
0.0016
0.0016
0.0017
0.0018
0.0018
0.0019
1
-2.8
0.0019
0.0020
0.0021
0.0021
0.0022
0.0023
0.0023
0.0024
0.0025
0.0026
-2.7
0.0026
0.0027
0.0028
0.0029
0.0030
0.0031
0.0032
0.0033
0.0034
0.0035
-2.6
0.0036
0.0037
0.0038
0.0039
0.0040
0.0041
0.0043
0.0044
0.0045
0.0047
-2.5
0.0048
0.0049
0.0051
0.0052
0.0054
0.0055
0.0057
0.0059
0.0060
0.0062
-2.4
0.0064
0.0066
0.0068
0.0069
0.0071
0.0073
0.0075
0.0078
0.0080
0.0082
-2.3
0.0084
0.0087
0.0089
0.0091
0.0094
0.0096
0.0099
0.0102
0.0104
0.0107
-22
0.0110
0.0113
0.0116
0.0119
0.0122
0.0125
0.0129
0.0132
0.0136
0.0139
-2.1
0.0143
0.0146
0.0150
0.0154
0.0158
0.0162
0.0166
0.0170
0.0174
0.0179
-2.0
0.0183
0.0188
0.0192
0.0197
0.0202
0.0207
0.0212
0.0217
0.0222
0.0228
-1.9
0.0233
0.0239
0.0244
0.0250
0.0256
0.0262
0.0268
0.0274
0.0281
0.0287
-1.8
0.0294
0.0301
0.0307
0.0314
0.0322
0.0329
0.0336
0.0344
0.0351
0.0359
2
The highlighted
value shows the area
-1.7
0.0367
0.0375
0.0384
0.0392
0.0401
0.0409
0.0418
0.0427
0.0436
0.0446
under the standard
-1.6
0.0455
0.0465
0.0475
0.0485
0.0495
0.0505
0.0516
0.0526
0.0537
0.0548
normal distribution
-1.5
0.0559
0.0571
0.0582
0.0594
0.0606
0.0618
0.0630
0.0643
0.0655
0.0668
below z-score -1.56.
-1.4
0.0681
0.0694
0.0708
0.0721
0.0735
0.0749
0.0764
0.0778
0.0793
0.0808
-1.3
0.0823
0.0838
0.0853
0.0869
0.0885
0.0901
0.0918
0.0934
0.0951
0.0968
-1.2
0.0985
0.1003
0.1020
0.1038
0.1056
0.1075
0.1093
0.1112
0.1131
0.1151
-1.1
0.1170
0.1190
0.1210
0.1230
0.1251
0.1271
0.1292
0.1314
0.1335
0.1357
-1.0
0.1379
0.1401
0.1423
0.1446
0.1469
0.1492
0.1515
0.1539
0.1562
0.1587
-0.9
0.1611
0.1635
0.1660
0.1685
0.1711
0.1736
0.1762
0.1788
0.1814
0.1841
-0.8
0.1867
0.1894
0.1922
0.1949
0.1977
0.2005
0.2033
0.2061
0.2090
0.2119
-0.7
0.2148
0.2177
0.2206
0.2236
0.2266
0.2296
0.2327
0.2358
0.2389
0.2420
-0.6
0.2451
0.2483
0.2514
0.2546
0.2578
0.2611
0.2643
0.2676
0.2709
0.2743
-0.5
0.2776
0.2810
0.2843
0.2877
0.2912
0.2946
0.2981
0.3015
0.3050
0.3085
-0.4
0.3121
0.3156
0.3192
0.3228
0.3264
0.3300
0.3336
0.3372
0.3409
0.3446
-0.3
0.3483
0.3520
0.3557
0.3594
0.3632
0.3669
0.3707
0.3745
0.3783
0.3821
-0.2
0.3859
0.3897
0.3936
0.3974
0.4013
0.4052
0.4090
0.4129
0.4168
0.4207
-0.1
0.4247
0.4286
0.4325
0.4364
0.4404
0.4443
0.4483
0.4522
0.4562
0.4602
-0.0
0.4641
0.4681
0.4721
0.4761
0.4801
0.4840
0.4880
0.4920
0.4960
0.5000
Note: For z < -3.70, use P(Z< z) z 0.0000
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