The mean cost of domestic airfares in the United States rose to an all-time high of $395 per ticket. Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of $115. Use Table 1 in Appendix B.a. What is the probability that a domestic airfare is $540 or more (to 4 decimals)?b. What is the probability that a domestic airfare is $240 or less (to 4 decimals)?c. What if the probability that a domestic airfare is between $300 and $490 (to 4 decimals)?d. What is the cost for the 5% highest domestic airfares? (rounded to nearest dollar) TABLE 1 CUMULATIVE PROBABILITIES FOR THE STANDARD NORMALDISTRIBUTIONEntries in the tablegive the area under thecurve to the left of thez value. For example, forz=-.85, the cumulativeprobability is .1977.Cumulativeprobability.00.01.0203.04.05.06.07.08.09-3.0.00130013.0013.00120012.0011.0011.0011.0010.0010-2.9.001900180018.0017.0016.0016.0015.0015.0014.0014.0026.0035-28.0025.0024.0023.0023.0022.0021.0021.0020.0019-2.70034.00330032.0031.0030.0029.0028.0027.0026-2.6.0047.0045.0044.0043.0041.0040.0039.0038.0037.0036-2.5.0062.0060.0059.0057.0055.0054.0052.0051.0049.0048-2.4.00820080.0078.0075.0073.0071.0069.0068.0066.0064.0102.009601250162-2.3.0107.0104.0099.0094.0091.0089.0087.0084-22-2.1.01390136.01320129.012201190116.0113.0110.0179.0174.0170.0166.0158.0154.0150.0146.0143-2.0.02280222.0217.0212.0207.0202.0197.0192.0188.0183.0256.0322.0250.0314-1.9.0287.0281.0274.0268.0262.0244.0239.0233-1.8.0359.0351.0344„0336.0329.0307.0301.0294-1.7.0446.0436.0427.04180409.0401.0375.0392.0485.0384.0367-1.6.05480537.0526.0516.0505.0495.04750465.0455-15.06680655.0643.0630.0618.0606.05940582.0571.0559-1.4.0808.0793.0778.07640749.0735.0721.0708.0694.0681-1.3.0968.0951.0934.0918.0901.0885.0869.0853.0838.0823-1.2.11511131.1112.1093.1075.1056.1038.1020.1003.0985-1.1.1357.1335.1314.1292.1271.1251.1230.1210.1190.1170-1.0.15871562.1539.1515.1492.1469.1446.1423.1401.1379-9.1841.1814.17881762.1736.1711.1685.1660.1635.1611-.821192090206120332005.1977.1949.1922.1894.1867-.7.242023892358.23272296.226622362206.21772148-627432709.2676.26432611.257825462514.24832451-530853050301529812946.2912.28772843.2810.2776-4.344634093372.3336330032643228319231563121-3.38213783374537073669.3632.35943557.35203483-242074168412940904052.401339743936389738594602456245224483444344044364432542864247-.0.5000496049204880484048014761472146814641 TABLE 1 CUMULATIVE PROBABILITIES FOR THE STANDARD NORMALDISTRIBUTION (Continued)CumulativeEntries in the tableprobabilitygive the area under thecurve to the left of thez value. For example, forz= 1.25, the cumulativeprobability is .8944..00.01.02.03.04.05.06.07.08.09.050005040.5080512051605199.52395279.5319.5359.55965987.53985438.5478.5517555756365675.571457532.5793.5832.5871.5910.5948.6026.6064.6103.6141.3.6179.6217.6255.6293.6331.6368.6406.6443.6480.65174.6554.6591.6628.6664.6700.6736.6772.6808.6844.6879.6915.6950.6985.7019.7054.7088.7123.7157.7190.7224.6.7257.7291.7324.7357.7389.7422.7454.74867517.7549.7.7580.7611.7642.7673.7704.7734.7764.7794.7823.7852.791080518315.8.7881.7939.7967.7995.8023.8078.8106.8133.9.8159.8186.8212.8238.8264.8289.8340.8365.83898438.8485.87081.0.8413.84618508.8531.85548577.859986211.1.8643.8665.86868729.8749.8770.8790.8810.88301.2.8849.8869.8888.8907.8925.8944.8962.8980.8997.90151.39032.9049.9066.90829099.9115.9131.9147.916291771.491929207.922292369251.9265.9279.9292.9306.93191.5.9332.9345.9357.9370.9382.9394.94069418.9429.94411.69452.9463.9474.94849495.9505.9515.95259535.95451.7.955495649573.95829591.95999608.9616.9625.9633.9706.97671.8.96419649.9656.96649671.9678.96869693.96991.9.9713.9719.9726.973297389744.9750.9756.9761.9783.9803.98462.0.9772.9778.97889793.9798.9808.9812.98172.1.9821.9826.9830.9834.9838.9842.9850.9854.98572.2.988198619893.9864.9868.9871.9875.9878.9884.9887.98902.3.9896.9898.9901.9904.99069909.9911.9913.99162.4.9918.9920.9922.9925.9927.9929.99319932.9934.99362.5.99389940.994199439945 99469948.9949.9951.99522.62.7.9953.9955.9956.9957.9959.9960.9961.9962.9963.9964.9965.9966.9967.99689969.9970.9971.9972.9973.99742.8.9974.9975 .9976.9977.9977.9978.9979.9979.9980.99812.9.9981.9982.9982.9983.9984.9984.9985.9985.9986.99863.09987.9987.9987.99889988.9989.9989.9989.99909990

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ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

The mean cost of domestic airfares in the United States rose to an all-time high of $395 per ticket. Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of $115. Use Table 1 in Appendix B.

a. What is the probability that a domestic airfare is $540 or more (to 4 decimals)?

b. What is the probability that a domestic airfare is $240 or less (to 4 decimals)?

c. What if the probability that a domestic airfare is between $300 and $490 (to 4 decimals)?

d. What is the cost for the 5% highest domestic airfares? (rounded to nearest dollar)

TABLE 1 CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL
DISTRIBUTION
Entries in the table
give the area under the
curve to the left of the
z value. For example, for
z=-.85, the cumulative
probability is .1977.
Cumulative
probability
.00
.01
.02
03
.04
.05
.06
.07
.08
.09
-3.0
.0013
0013
.0013
.0012
0012
.0011
.0011
.0011
.0010
.0010
-2.9
.0019
0018
0018
.0017
.0016
.0016
.0015
.0015
.0014
.0014
.0026
.0035
-28
.0025
.0024
.0023
.0023
.0022
.0021
.0021
.0020
.0019
-2.7
0034
.0033
0032
.0031
.0030
.0029
.0028
.0027
.0026
-2.6
.0047
.0045
.0044
.0043
.0041
.0040
.0039
.0038
.0037
.0036
-2.5
.0062
.0060
.0059
.0057
.0055
.0054
.0052
.0051
.0049
.0048
-2.4
.0082
0080
.0078
.0075
.0073
.0071
.0069
.0068
.0066
.0064
.0102
.0096
0125
0162
-2.3
.0107
.0104
.0099
.0094
.0091
.0089
.0087
.0084
-22
-2.1
.0139
0136
.0132
0129
.0122
0119
0116
.0113
.0110
.0179
.0174
.0170
.0166
.0158
.0154
.0150
.0146
.0143
-2.0
.0228
0222
.0217
.0212
.0207
.0202
.0197
.0192
.0188
.0183
.0256
.0322
.0250
.0314
-1.9
.0287
.0281
.0274
.0268
.0262
.0244
.0239
.0233
-1.8
.0359
.0351
.0344
„0336
.0329
.0307
.0301
.0294
-1.7
.0446
.0436
.0427
.0418
0409
.0401
.0375
.0392
.0485
.0384
.0367
-1.6
.0548
0537
.0526
.0516
.0505
.0495
.0475
0465
.0455
-15
.0668
0655
.0643
.0630
.0618
.0606
.0594
0582
.0571
.0559
-1.4
.0808
.0793
.0778
.0764
0749
.0735
.0721
.0708
.0694
.0681
-1.3
.0968
.0951
.0934
.0918
.0901
.0885
.0869
.0853
.0838
.0823
-1.2
.1151
1131
.1112
.1093
.1075
.1056
.1038
.1020
.1003
.0985
-1.1
.1357
.1335
.1314
.1292
.1271
.1251
.1230
.1210
.1190
.1170
-1.0
.1587
1562
.1539
.1515
.1492
.1469
.1446
.1423
.1401
.1379
-9
.1841
.1814
.1788
1762
.1736
.1711
.1685
.1660
.1635
.1611
-.8
2119
2090
2061
2033
2005
.1977
.1949
.1922
.1894
.1867
-.7
.2420
2389
2358
.2327
2296
.2266
2236
2206
.2177
2148
-6
2743
2709
.2676
.2643
2611
.2578
2546
2514
.2483
2451
-5
3085
3050
3015
2981
2946
.2912
.2877
2843
.2810
.2776
-4
.3446
3409
3372
.3336
3300
3264
3228
3192
3156
3121
-3
.3821
3783
3745
3707
3669
.3632
.3594
3557
.3520
3483
-2
4207
4168
4129
4090
4052
.4013
3974
3936
3897
3859
4602
4562
4522
4483
4443
4404
4364
4325
4286
4247
-.0
.5000
4960
4920
4880
4840
4801
4761
4721
4681
4641

TABLE 1 CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL
DISTRIBUTION (Continued)
Cumulative
Entries in the table
probability
give the area under the
curve to the left of the
z value. For example, for
z= 1.25, the cumulative
probability is .8944.
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
.0
5000
5040
.5080
5120
5160
5199
.5239
5279
.5319
.5359
.5596
5987
.5398
5438
.5478
.5517
5557
5636
5675
.5714
5753
2
.5793
.5832
.5871
.5910
.5948
.6026
.6064
.6103
.6141
.3
.6179
.6217
.6255
.6293
.6331
.6368
.6406
.6443
.6480
.6517
4
.6554
.6591
.6628
.6664
.6700
.6736
.6772
.6808
.6844
.6879
.6915
.6950
.6985
.7019
.7054
.7088
.7123
.7157
.7190
.7224
.6
.7257
.7291
.7324
.7357
.7389
.7422
.7454
.7486
7517
.7549
.7
.7580
.7611
.7642
.7673
.7704
.7734
.7764
.7794
.7823
.7852
.7910
8051
8315
.8
.7881
.7939
.7967
.7995
.8023
.8078
.8106
.8133
.9
.8159
.8186
.8212
.8238
.8264
.8289
.8340
.8365
.8389
8438
.8485
.8708
1.0
.8413
.8461
8508
.8531
.8554
8577
.8599
8621
1.1
.8643
.8665
.8686
8729
.8749
.8770
.8790
.8810
.8830
1.2
.8849
.8869
.8888
.8907
.8925
.8944
.8962
.8980
.8997
.9015
1.3
9032
.9049
.9066
.9082
9099
.9115
.9131
.9147
.9162
9177
1.4
9192
9207
.9222
9236
9251
.9265
.9279
.9292
.9306
.9319
1.5
.9332
.9345
.9357
.9370
.9382
.9394
.9406
9418
.9429
.9441
1.6
9452
.9463
.9474
.9484
9495
.9505
.9515
.9525
9535
.9545
1.7
.9554
9564
9573
.9582
9591
.9599
9608
.9616
.9625
.9633
.9706
.9767
1.8
.9641
9649
.9656
.9664
9671
.9678
.9686
9693
.9699
1.9
.9713
.9719
.9726
.9732
9738
9744
.9750
.9756
.9761
.9783
.9803
.9846
2.0
.9772
.9778
.9788
9793
.9798
.9808
.9812
.9817
2.1
.9821
.9826
.9830
.9834
.9838
.9842
.9850
.9854
.9857
2.2
.9881
9861
9893
.9864
.9868
.9871
.9875
.9878
.9884
.9887
.9890
2.3
.9896
.9898
.9901
.9904
.9906
9909
.9911
.9913
.9916
2.4
.9918
.9920
.9922
.9925
.9927
.9929
.9931
9932
.9934
.9936
2.5
.9938
9940
.9941
9943
9945 9946
9948
.9949
.9951
.9952
2.6
2.7
.9953
.9955
.9956
.9957
.9959
.9960
.9961
.9962
.9963
.9964
.9965
.9966
.9967
.9968
9969
.9970
.9971
.9972
.9973
.9974
2.8
.9974
.9975 .9976
.9977
.9977
.9978
.9979
.9979
.9980
.9981
2.9
.9981
.9982
.9982
.9983
.9984
.9984
.9985
.9985
.9986
.9986
3.0
9987
.9987
.9987
.9988
9988
.9989
.9989
.9989
.9990
9990

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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