Answered: An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 140lb and 191 lb. The new population of…

MATLAB: An Introduction with Applications

6th Edition

ISBN: 9781119256830

Author: Amos Gilat

Publisher: John Wiley & Sons Inc

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Question

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 140lb and 191 lb. The new population of pilots has normally distributed weights with a mean of 147 lb
and a standard deviation of 28.9 lb.

Pictures of Charts are attached for the standard normal distribution.

a. If a pilot is randomly selected, find the probability that his weight is between 140lb and 191 lb.

The probability is approximately?
(Round to four decimal places as needed.)

b. If 40 different pilots are randomly selected, find the probability that their mean weight is between 140 lb and 191lb.

The probability is approximately
(Round to four decimal places as needed.)

c. When redesigning the ejection seat, which probability is more relevant?

Choose one from below.

Part (a) because the seat performance for a sample of pilots is more important.

Part (b) because the seat performance for a sample of pilots is more important.

Part (a) because the seat performance for a single pilot is more important.

Part (b) because the seat performance for a single pilot is more important.

0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.5
0.504
0.508
0.512
0.516
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
0.591
0.5948
0.5987
0.6026
0.6064
0.6103
0.6141
0.3
0.6179
0.6217
0.6255
0.6293
0.6331
0.6368
0.6406
0.6443
0.648
0.6517
0.4
0.6554
0.6591
0.6628
0.6664
0.67
0.6736
0.6772
0.6808
0.6844
0.6879
0.5
0.6915
0.695
0.6985
0.7019
0.7054
0.7088
0.7123
0.7157
0.719
0.7224
0.6
0.7257
0.7291
0.7324
0.7357
0.7389
0.7422
0.7454
0.7486
0.7517
0.7549
0.7
0.758
0.7611
0.7642
0.7673
0.7704
0.7734
0.7764
0.7794
0.7823
0.7852
0.8
0.7881
0.791
0.7939
0.7967
0.7995
0.8023
0.8051
0.8078
0.8106
0.8133
0.9
0.8159
0.8186
0.8212
0.8238
0.8264
0.8289
0.8315
0.834
0.8365
0.8389
1.
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
0.877
0.879
0.881
0.883
1.2
0.8849
0.8869
0.8888
0.8907
0.8925
0.8944
0.8962
0.898
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
0.937
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
1.9
0.9713
0.9719
0.9726
0.9732
0.9738
0.9744
0.975
0.9756
0.9761
0.9767
2.
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
0.983
0.9834
0.9838
0.9842
0.9846
0.985
0.9854
0.9857
2.2
0.9861
0.9864
0.9868
0.9871
0.9875
0.9878
0.9881
0.9884
0.9887
0.989
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
0.992
0.9922
0.9925
0.9927
0.9929
0.9931
0.9932
0.9934
0.9936
2.5
0.9938
0.994
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
0.996
0.9961
0.9962
0.9963
0.9964
2.7
0.9965
0.9966
0.9967
0.9968
0.9969
0.997
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
0.998
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
0.9987
0.9987
0.9987
0.9988
0.9988
0.9989
0.9989
0.9989
0.999
0.999
3.1
0.999
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 and up
0.9999

0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
-3.5 and lower
0.0001
-3.4
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0002
-3.3
0.0005
0.0005
0.0005
0.0004
0.0004
0.0004
0.0004
0.0004
0.0004
0.0003
0.0006
0.0008
-3.2
0.0007
0.0007
0.0006
0.0006
0.0006
0.0006
0.0005
0.0005
0.0005
-3.1
0.001
0.0009
0.0009
0.0008
0.0007
0.0009
0.0008
0.0008
0.0007
-3
0.0013
0.0013
0.0013
0.0012
0.0012
0.0011
0.0011
0.0011
0.001
0.001
-2.9
0.0019
0.0018
0.0018
0.0017
0.0016
0.0016
0.0015
0.0015
0.0014
0.0014
-2.8
0.0026
0.0025
0.0024
0.0023
0.0023
0.0022
0.0021
0.0021
0.002
0.0019
-2.7
0.0035
0.0034
0.0033
0.0032
0.0031
0.003
0.0029
0.0028
0.0027
0.0026
-2.6
0.0047
0.0045
0.0044
0.0043
0.0041
0.004
0.0039
0.0038
0.0037
0.0036
0.0051
0.0068
-2.
0.0062
0.006
0.0059
0.0057
0.0055
0.0054
0.0052
0.0049
0.0048
-2.4
0.0082
0.008
0.0078
0.0075
0.0073
0.0071
0.0069
0.0066
0.0064
0.0091
0.0119
-2.3
0.0107
0.0104
0.0102
0.0099
0.0096
0.0094
0.0089
0.0087
0.0084
-2.2
0.0139
0.0136
0.0132
0.0129
0.0125
0.0122
0.0116
0.0113
0.011
-2.1
0.0179
0.0174
0.017
0.0166
0.0162
0.0158
0.0154
0.015
0.0146
0.0143
-2
0.0228
0.0222
0.0217
0.0212
0.0207
0.0202
0.0197
0.0192
0.0188
0.0183
-1.9
0.0287
0.0281
0.0274
0.0268
0.0262
0.0256
0.025
0.0244
0.0239
0.0233
-1.8
0.0359
0.0351
0.0344
0.0336
0.0329
0.0322
0.0314
0.0307
0.0301
0.0294
-1.7
0.0446
0.0436
0.0427
0.0418
0.0409
0.0401
0.0392
0.0384
0.0375
0.0367
-1.6
0.0548
0.0537
0.0526
0.0516
0.0505
0.0495
0.0485
0.0475
0.0465
0.0455
-1.5
0.0668
0.0655
0.0643
0.063
0.0618
0.0606
0.0594
0.0582
0.0571
0.0559
-1.4
0.0808
0.0793
0.0778
0.0764
0.0749
0.0735
0.0721
0.0708
0.0694
0.0681
-1.3
0.0968
0.0951
0.0934
0.0918
0.0901
0.0885
0.0869
0.0853
0.0838
0.0823
-1.2
0.1151
0.1131
0.1112
0.1093
0.1075
0.1056
0.1038
0.102
0.1003
0.0985
-1.1
0.1357
0.1335
0.1314
0.1292
0.1271
0.1251
0.123
0.121
0.119
0.117
-1
0.1587
0.1562
0.1539
0.1515
0.1492
0.1469
0.1446
0.1423
0.1401
0.1379
-0.9
0.1841
0.1814
0.1788
0.1762
0.1736
0.1711
0.1685
0.166
0.1635
0.1611
-0.8
0.2119
0.209
0.2061
0.2033
0.2005
0.1977
0.1949
0.1922
0.1894
0.1867
-0.7
0.242
0.2389
0.2358
0.2327
0.2296
0.2266
0.2236
0.2206
0.2177
0.2148
-0.6
0.2743
0.2709
0.2676
0.2643
0.2611
0.2578
0.2546
0.2514
0.2483
0.2451
-0.5
0.3085
0.305
0.3015
0.2981
0.2946
0.2912
0.2877
0.2843
0.281
0.2776
-0.4
0.3446
0.3409
0.3372
0.3336
0.33
0.3264
0.3228
0.3192
0.3156
0.3121
-0.3
0.3821
0.3783
0.3745
0.3707
0.3669
0.3632
0.3594
0.3557
0.352
0.3483
-0.2
0.4207
0.4168
0.4129
0.409
0.4052
0.4013
0.3974
0.3936
0.3897
0.3859
-0.1
0.4602
0.4562
0.4522
0.4483
0.4443
0.4404
0.4364
0.4325
0.4286
0.4247
0.5
0.496
0.492
0.488
0.484
0.4801
0.4761
0.4721
0.4681
0.4641

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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