The mean cost of domestic airfares in the United States rose to an all-time high of $385 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 $100. 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 $500 (to 4 decimals)?d. What is the cost for the 3% highest domestic airfares? (rounded to nearest dollar) TABLE 1 CUMULATIVE PROBABILITIES FOR THE STANDARD NORMALDISTRIBUTIONEntries in the table Qgive the area under thecurve to the left of theCumulativeprobabilityz value. For example, forz=-.85, the cumulativeprobability is .1977..00.01.02.03.04.05.06.07.08.09-3.0.0013.0013.0013.0012.0012.0011.0011.0011.0010.0010-2.9.0019.0018.0018.0017.0016.0016.0015.0015.0014.0014-2.8.0026.0025.0024.0023.0023.0022.0021.0021.0020.0019-2.7.0035.0034.0033.0032.0031.0030.0029.0028.0027.0026-2.6.0047.0045.0044.0043.0041.0040.0039.0038.0037.0036-2.5.0062.0060.0059.0057.0055.0054.0052.0051.0049.0048-24.0082.0080.0078.0075.0073.0071.0069.0068.0066.0064-2.3.0107.0104.0102.0099.0096.0094.0091.0089.0087.0084-2.2.0139.0136.0132.0129.0125.0122.0119.0116.0113.0110-2.1.0179.0174.0170.0166.0162.0158.0154.0150.0146.0143-2.0.0228.0222.0217.0212.0207.0202.0197.0192.0188.0183-1.9.0287.0281.0274.0268.0262.0256.0250.0244.0239.0233-1.8.0359.0351.0344.0336.0329.0322.0314.0307.0301.0294.0375.0465-1.7.0446.0436.0427.0418.0409.0401.0392.0384.0367-1.6-1.5.0548.0537.0526.0516.0505.0495.0485.0475.0455.0668.0655.0643.0630.0618.0606.0594.0582.0571.0559-1.4.0808.0793.0778.0764.0749.0735.0721.0708.0694.0681-1.3.0968.0951.0934.0918.0901.0885.0869.0853.0838.0823-1.2.1151.1131.1112.1093.1075.1056.1038.1020.1003.0985-1.1.1357.1335.1314.1292.1271.1251.1230.1210.1190.1170-1.0.1587.1562.1539.1515.1492.1469.1446.1423.1401.1379-9.1841.1814.1788.1762.1736.1711.1685.1660.1635.1611-.8.2119.2090.2061.20332005.1977.1949.1922.1894.1867-.7.2420.2389.2358.2327.2296.2266.2236.2206.2177.2148-.6.2743.2709.2676.2643.26112578.2546.2514.24832451-5.3085.3050.3015.2981.2946.2912.2877.2843.2810.2776-43446.3409.3372.3336.3300.3264.3228.3192.3156.3121-3.3821.3783.3745.3707.3669.3632.3594.3557.3520.3483.4052.4443-2.4207.41684129.40904013.3974.3936.3897.3859-1.4602.4562.4522448344044364.4325.42864247-.0.5000.4960.4920.4880.484048014761.4721.4681.4641 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..00.01.02.03.04.05.06.07.08.09.0.5000.5040.5080.5120.5160.5199.5239.5279.5319.5359.1.5398.5438.5478.5517.55575596.5636.5675.5714.5753.2.5793.5832.5871.5910.5948.5987.6026.6064.6103.6141.3.6179.6217.6255.6293.6331.6368.6406.6443.6480.6517.4.6554.6591.6628.6664.6700.6736.6772.6808.6844.6879.5.6915.6950.6985.7019.7054.7088.7123.7157.7190.7224.6.7257.7291.7324.7357.7389.7422.7454.7486.7517.7549.7.7580.7611.7642.7673.7704.7734.7764.7794.7823.7852.8.7881.7910.7939.7967.7995.8023.8051.8078.8106.8133.9.8159.8186.8212.8238.8264.8289.8315.8340.8365.8389.8554.857787901.0.8413.8438.8461.8485.8508.8531.8599.86211.1.8643.8665.8686.8708.8729.8749.8770.8810.88301.2.8849.8869.8888.8907.8925.8944.8962.8980.8997.90151.3.9032.9049.9066.908290999115.9131.9147.9162.91771.4.9192.9207.9222.9236.9251.92659279.9292.930693191.5.9332.9345.9357.9370.9382.9394.9406.9418.94299535.94411.6.9452.9463.9474.9484.9495.9505.9515.9525.9545.961696931.7.9554.9564.9573.9582.9591.9599.9608.9625.96331.8.9641.9649.9656.9664.9671.9678.9686.9699.97061.9.9713.9719.9726.9732.9738.9744.9750.97569761.9767.9808.98502.0.9772.9778.9783.9788.9793.9798.9803.9812.98172.1.9821.9826.9830.9834.9838.9842.9846.9854.98572.2.9861.9864.9868.9871.9875.9878.9881.9884.9887.98902.3.9893.9896.9898.9901.9904.9906.9909.9911.9913.99162.49918.9920.9922.9925.9927.9929.9931.9932.9934.99362.5.9938.9940.9941.9943.99459946.9948.9949.9951.995299559961.9964.99742.6.9953.9956.9957.9959.99609962.9963.99732.7.9965.9966.9967.9968.9969.9970.9971.99722.8.9974.9975.9976.9977.9977.9978.9979.9979.9980.99812.9.9981.9982.9982.9983.9984.9984.9985.9985.9986.99863.0.9987.9987.9987.9988.9988.9989.9989.9989.9990.9990of

Let X be a random variable such that X: Cost of domestic airfares in the United States X~N385, 1002…

Answered: The mean cost of domestic airfares in…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Concept explainers

Question

The mean cost of domestic airfares in the United States rose to an all-time high of $385 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 $100. 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 $500 (to 4 decimals)?

d. What is the cost for the 3% highest domestic airfares? (rounded to nearest dollar)

TABLE 1 CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL
DISTRIBUTION
Entries in the table Q
give the area under the
curve to the left of the
Cumulative
probability
z value. For example, for
z=-.85, the cumulative
probability is .1977.
.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
-2.8
.0026
.0025
.0024
.0023
.0023
.0022
.0021
.0021
.0020
.0019
-2.7
.0035
.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
-24
.0082
.0080
.0078
.0075
.0073
.0071
.0069
.0068
.0066
.0064
-2.3
.0107
.0104
.0102
.0099
.0096
.0094
.0091
.0089
.0087
.0084
-2.2
.0139
.0136
.0132
.0129
.0125
.0122
.0119
.0116
.0113
.0110
-2.1
.0179
.0174
.0170
.0166
.0162
.0158
.0154
.0150
.0146
.0143
-2.0
.0228
.0222
.0217
.0212
.0207
.0202
.0197
.0192
.0188
.0183
-1.9
.0287
.0281
.0274
.0268
.0262
.0256
.0250
.0244
.0239
.0233
-1.8
.0359
.0351
.0344
.0336
.0329
.0322
.0314
.0307
.0301
.0294
.0375
.0465
-1.7
.0446
.0436
.0427
.0418
.0409
.0401
.0392
.0384
.0367
-1.6
-1.5
.0548
.0537
.0526
.0516
.0505
.0495
.0485
.0475
.0455
.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
.4052
.4443
-2
.4207
.4168
4129
.4090
4013
.3974
.3936
.3897
.3859
-1
.4602
.4562
.4522
4483
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
.1
.5398
.5438
.5478
.5517
.5557
5596
.5636
.5675
.5714
.5753
.2
.5793
.5832
.5871
.5910
.5948
.5987
.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
.5
.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
.8
.7881
.7910
.7939
.7967
.7995
.8023
.8051
.8078
.8106
.8133
.9
.8159
.8186
.8212
.8238
.8264
.8289
.8315
.8340
.8365
.8389
.8554
.8577
8790
1.0
.8413
.8438
.8461
.8485
.8508
.8531
.8599
.8621
1.1
.8643
.8665
.8686
.8708
.8729
.8749
.8770
.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
9535
.9441
1.6
.9452
.9463
.9474
.9484
.9495
.9505
.9515
.9525
.9545
.9616
9693
1.7
.9554
.9564
.9573
.9582
.9591
.9599
.9608
.9625
.9633
1.8
.9641
.9649
.9656
.9664
.9671
.9678
.9686
.9699
.9706
1.9
.9713
.9719
.9726
.9732
.9738
.9744
.9750
.9756
9761
.9767
.9808
.9850
2.0
.9772
.9778
.9783
.9788
.9793
.9798
.9803
.9812
.9817
2.1
.9821
.9826
.9830
.9834
.9838
.9842
.9846
.9854
.9857
2.2
.9861
.9864
.9868
.9871
.9875
.9878
.9881
.9884
.9887
.9890
2.3
.9893
.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
9955
9961
.9964
.9974
2.6
.9953
.9956
.9957
.9959
.9960
9962
.9963
.9973
2.7
.9965
.9966
.9967
.9968
.9969
.9970
.9971
.9972
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
of

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.

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.