A new version of the Medical College Admissions Test (MCAT) was introduced in spring 2015 and is intended to shift the focus from what applicants know to how well they can use what they know. One result of the change is that the scale on which the exam is graded was modified, with the total score of the four sections on the test ranging from 472 to 528. In spring 2015, the mean score was 500.0 with a standard deviation of 10.6. (a) Assuming that the MCAT scores are normally distributed, use Table A to find the median and the first and third quartiles of the MCAT scores.Find the median of the MCAT scores. (Enter your answer rounded to a whole number.) median= Find the first quartile of the MCAT scores. (Enter your answer rounded to three decimal places.) Q1= Find the third quartile of the MCAT scores. (Enter your answer rounded to three decimal places.) Q3= Find the interquartile range of the MCAT scores. (Enter your answer rounded to three decimal places.) IQR= (b) Which interval contains the central 80%80% of the MCAT scores? Select the answer choice that approximates this interval. A) 491.096 to 508.904B) 472 to 528C) 480 to 520D) 486.432 to 513.568 696TABLESTable entry for z is the area under theTable entrystandard Normal curve to the left of z.TABLE A Standard normal cumulative proportions.00.01.02.03.04.05.06.07.08.09-3.4.0003.0003.0003.0003.0003.0003.0003.0003.0003.0002.0003.0005.0007.0005.0004.0006-3.3.0005.0005.0004.0004.0004.0004.0004-3.2.0007.0007.0006.0006.0006.0006.0005.0005-3.1.0010.0009.0009.0009.0008.0008.0008.0008.0007-3.0.0013.0013.0013.0012.0012.0011.0011.0011.0010.0010-2.9.0019.0018.0018.0017.0016.0016.0015.0015.0014.0014.0023.0032-2.8.0026.0025.0024.0023.0022.0021.0021.0020.0019-2.7.0035.0034.0033.0031.0030.0029.0028.0027.0026-2.6.0047.0045.0044.0043.0041.0040.0054.0039.0038.0037.0036-2.5.0062.0060.0059.0057.0055.0052.0051.0049.0048-2.4.0064.0084.0082.0080.0078.0075.0073.0071.0069.0068.0066-2.3.0107.0104.0102.0099.0096.0094.0091.0089.0087-2.2.0139.0136.0132.0129.0125.0122.0119.0116.0113.0110.0174.0222.0170.0217-2.1.0179.0166.0162.0158.0154.0150.0146.0143-2.0.0228.0212.0207.0202.0197.0192.0188.0183.0274.0287.0359.0281.0268.0262.0256.0250.0233.0244.0307.0384-1.9.0239.0314- 1.8- 1.7.0336.0418.0516.0329.0409.0351.0344.0322.0301.0294.0446.0436.0427.0401.0392.0375.0367.0485.0505.0618.0455.0548.0668-1.6.0537.0526.0495.0475.0465-1.5.0655.0643.0630.0606.0594.0582.0571.0559-1.4-1.3.0694.0838.0808.0793.0778.0764.0749.0735.0721.0708.0681.0968.0951.0934.0918.0901.0885.0869.0853.0823- 1.2- 1.1.1038.1230.1151.1131.1112.1093.1075.1056.1020.1003.0985.1357.1335.1314.1292.1271.1251.1210.1190.1170-1.0.1587.1562.1539.1515.1492.1469.1446.1423.1401.1379.1814.2090-0.9.1841.1788.1762.1736.1711.1685.1660.1635.1611-0.8.2119.2061.2033.2005.1977.1949.1922.1894.1867-0.7.2420.2389.2358.2327.2296.2266.2236.2206.2177.2148-0.6.2743.2709.2676.2643.2611.2578.2546.2514.2483.2451-0.530853050.3015.2981.2946.2912.2877.2843.2810.2776.3409.3783.4168-0.4.3446.3372.33363300.3264.3228.3192.3156.3121-0.3.3821.37453707.3669.3632.3594.35573520.3483.4090.4483.4880-0.2.4207.4129.4052.4013.3974.3936.3897.3859.4404.4801.4247.4641-0.1.4602.4562.4522.4443.4364.4325.4286-0.0.5000.4960.4920.4840.4761.4721.4681 TABLES697Table entryTable entry for z is the area under thestandard Normal curve to the left of z.TABLE A Standard Normal cumulative proportions (continued).00.01.02.03.04.05.06.07.08.090.0.5000.5040.5080.5120.5160.5199.5239.5279.5319.5359.5557.5948.6331.5636.60260.1.5398.5438.5478.5517.5596.5675.5714.57530.2.5793.5832.5871.5910.5987.6064.6103.61410.30.4.6406.6772.6480.6844.6179.6217.6255.6293.6368.6443.6517.6554.6591.6628.6664.6700.6736.6808.6879.6950.7054.7389.7088.7422.7123.7454.77640.5.6915.6985.7019.7157.7190.72240.6.7257.7580.7517.7823.8106.7291.7324.7357.7486.7794.8078.8340.75490.7.7611.7642.7673.7704.7734.7852.8023.82890.8.7881.7910.7939.7967.7995.8051.81330.9.8159.8186.8212.8238.8264.8315.8365.8389.8485.8708.8907.8508.8577.87901.0.8413.8438.8461.8531.8554.8599.8621.8643.8849.8749.89441.1.8665.8686.8729.8770.8810.88301.2.8869.8888.8925.8962.8980.8997.90151.3.9032.9049.9066.9082.9099.9115.9131.9147.9162.91771.4.9192.9207.9222.9236.9251.9265.9279.9292.9306.93191.5.9332.9345.9357.9370.9382.9394.9406.9418.9429.9441.9463.95641.6.9452.9474.9484.9495.9505.9515.9525.9535.95451.7.9554.9573.9582.9591.9599.9608.9616.9625.9633.9678.97441.8.9641.9649.9656.9664.9671.9686.9693.9699.97061.9.9713.9719.9726.9732.9738.9750.9756.9761.97672.0.9772.9778.9783.9788.9793.9798.9803.9808.9812.98172.1.9821.9826.9830.9834.9838.9842.9846.9850.9854.9887.9913.98572.2.9861.9864.9868.9871.9875.9878.9881.9884.98902.3.9893.9896.9898.9901.9904.9906.9909.9911.99162.4.9918.9920.9922.9925.9927.9929.9931.9932.9934.99362.5.9938.9940.9941.9943.9945.9946.9948.9949.9951.99522.6.9953.9955.9956.9957.9959.9960.9961.9962.9963.99642.7.9965.9966.9967.9968.9969.9970.9971.9972.9973.9974.9977.99832.8.9974.9975.9976.9977.9978.9979.9979.9980.99812.9.9981.9982.9982.9984.9984.9985.99859986.99863.0.9987.9987.9987.99889988.9989.9989.9989.9990.99903.1.9990.9991.9991.9991.9992.9992.9992.9992.9993.99933.2.9993.9993.9994.9994.9994.9994.9994.9996.9995.9995.99953.3.9995.9995.9995.9996.9996.9996.9996.9996.99973.4.9997.9997.9997.9997.9997.9997.9997.9997.9997.9998

Name: A new version of the Medical College Admissions Test (MCAT) was introd
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Description: A new version of the Medical College Admissions Test (MCAT) was introduced in spring 2015 and is intended to shift the focus from what applicants know to how well they can use what they know. One result of the change is that the scale on which the ex

Quartiles: The observations Q1, Q2, And Q3 which divide the total number of observations into 4…

Answered: A new version of the Medical College…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A new version of the Medical College Admissions Test (MCAT) was introduced in spring 2015 and is intended to shift the focus from what applicants know to how well they can use what they know. One result of the change is that the scale on which the exam is graded was modified, with the total score of the four sections on the test ranging from 472 to 528. In spring 2015, the mean score was 500.0 with a standard deviation of 10.6.

(a) Assuming that the MCAT scores are normally distributed, use Table A to find the median and the first and third quartiles of the MCAT scores.

Find the median of the MCAT scores.

(Enter your answer rounded to a whole number.)

median=

Find the first quartile of the MCAT scores. (Enter your answer rounded to three decimal places.)

Q1=

Find the third quartile of the MCAT scores. (Enter your answer rounded to three decimal places.)

Q3=

Find the interquartile range of the MCAT scores. (Enter your answer rounded to three decimal places.)

IQR=

(b) Which interval contains the central 80%80% of the MCAT scores? Select the answer choice that approximates this interval.

A) 491.096 to 508.904

B) 472 to 528

C) 480 to 520

D) 486.432 to 513.568

696
TABLES
Table entry for z is the area under the
Table entry
standard Normal curve to the left of z.
TABLE A Standard normal cumulative proportions
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
-3.4
.0003
.0003
.0003
.0003
.0003
.0003
.0003
.0003
.0003
.0002
.0003
.0005
.0007
.0005
.0004
.0006
-3.3
.0005
.0005
.0004
.0004
.0004
.0004
.0004
-3.2
.0007
.0007
.0006
.0006
.0006
.0006
.0005
.0005
-3.1
.0010
.0009
.0009
.0009
.0008
.0008
.0008
.0008
.0007
-3.0
.0013
.0013
.0013
.0012
.0012
.0011
.0011
.0011
.0010
.0010
-2.9
.0019
.0018
.0018
.0017
.0016
.0016
.0015
.0015
.0014
.0014
.0023
.0032
-2.8
.0026
.0025
.0024
.0023
.0022
.0021
.0021
.0020
.0019
-2.7
.0035
.0034
.0033
.0031
.0030
.0029
.0028
.0027
.0026
-2.6
.0047
.0045
.0044
.0043
.0041
.0040
.0054
.0039
.0038
.0037
.0036
-2.5
.0062
.0060
.0059
.0057
.0055
.0052
.0051
.0049
.0048
-2.4
.0064
.0084
.0082
.0080
.0078
.0075
.0073
.0071
.0069
.0068
.0066
-2.3
.0107
.0104
.0102
.0099
.0096
.0094
.0091
.0089
.0087
-2.2
.0139
.0136
.0132
.0129
.0125
.0122
.0119
.0116
.0113
.0110
.0174
.0222
.0170
.0217
-2.1
.0179
.0166
.0162
.0158
.0154
.0150
.0146
.0143
-2.0
.0228
.0212
.0207
.0202
.0197
.0192
.0188
.0183
.0274
.0287
.0359
.0281
.0268
.0262
.0256
.0250
.0233
.0244
.0307
.0384
-1.9
.0239
.0314
- 1.8
- 1.7
.0336
.0418
.0516
.0329
.0409
.0351
.0344
.0322
.0301
.0294
.0446
.0436
.0427
.0401
.0392
.0375
.0367
.0485
.0505
.0618
.0455
.0548
.0668
-1.6
.0537
.0526
.0495
.0475
.0465
-1.5
.0655
.0643
.0630
.0606
.0594
.0582
.0571
.0559
-1.4
-1.3
.0694
.0838
.0808
.0793
.0778
.0764
.0749
.0735
.0721
.0708
.0681
.0968
.0951
.0934
.0918
.0901
.0885
.0869
.0853
.0823
- 1.2
- 1.1
.1038
.1230
.1151
.1131
.1112
.1093
.1075
.1056
.1020
.1003
.0985
.1357
.1335
.1314
.1292
.1271
.1251
.1210
.1190
.1170
-1.0
.1587
.1562
.1539
.1515
.1492
.1469
.1446
.1423
.1401
.1379
.1814
.2090
-0.9
.1841
.1788
.1762
.1736
.1711
.1685
.1660
.1635
.1611
-0.8
.2119
.2061
.2033
.2005
.1977
.1949
.1922
.1894
.1867
-0.7
.2420
.2389
.2358
.2327
.2296
.2266
.2236
.2206
.2177
.2148
-0.6
.2743
.2709
.2676
.2643
.2611
.2578
.2546
.2514
.2483
.2451
-0.5
3085
3050
.3015
.2981
.2946
.2912
.2877
.2843
.2810
.2776
.3409
.3783
.4168
-0.4
.3446
.3372
.3336
3300
.3264
.3228
.3192
.3156
.3121
-0.3
.3821
.3745
3707
.3669
.3632
.3594
.3557
3520
.3483
.4090
.4483
.4880
-0.2
.4207
.4129
.4052
.4013
.3974
.3936
.3897
.3859
.4404
.4801
.4247
.4641
-0.1
.4602
.4562
.4522
.4443
.4364
.4325
.4286
-0.0
.5000
.4960
.4920
.4840
.4761
.4721
.4681

TABLES
697
Table entry
Table entry for z is the area under the
standard Normal curve to the left of z.
TABLE A Standard Normal cumulative proportions (continued)
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
0.0
.5000
.5040
.5080
.5120
.5160
.5199
.5239
.5279
.5319
.5359
.5557
.5948
.6331
.5636
.6026
0.1
.5398
.5438
.5478
.5517
.5596
.5675
.5714
.5753
0.2
.5793
.5832
.5871
.5910
.5987
.6064
.6103
.6141
0.3
0.4
.6406
.6772
.6480
.6844
.6179
.6217
.6255
.6293
.6368
.6443
.6517
.6554
.6591
.6628
.6664
.6700
.6736
.6808
.6879
.6950
.7054
.7389
.7088
.7422
.7123
.7454
.7764
0.5
.6915
.6985
.7019
.7157
.7190
.7224
0.6
.7257
.7580
.7517
.7823
.8106
.7291
.7324
.7357
.7486
.7794
.8078
.8340
.7549
0.7
.7611
.7642
.7673
.7704
.7734
.7852
.8023
.8289
0.8
.7881
.7910
.7939
.7967
.7995
.8051
.8133
0.9
.8159
.8186
.8212
.8238
.8264
.8315
.8365
.8389
.8485
.8708
.8907
.8508
.8577
.8790
1.0
.8413
.8438
.8461
.8531
.8554
.8599
.8621
.8643
.8849
.8749
.8944
1.1
.8665
.8686
.8729
.8770
.8810
.8830
1.2
.8869
.8888
.8925
.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
.9463
.9564
1.6
.9452
.9474
.9484
.9495
.9505
.9515
.9525
.9535
.9545
1.7
.9554
.9573
.9582
.9591
.9599
.9608
.9616
.9625
.9633
.9678
.9744
1.8
.9641
.9649
.9656
.9664
.9671
.9686
.9693
.9699
.9706
1.9
.9713
.9719
.9726
.9732
.9738
.9750
.9756
.9761
.9767
2.0
.9772
.9778
.9783
.9788
.9793
.9798
.9803
.9808
.9812
.9817
2.1
.9821
.9826
.9830
.9834
.9838
.9842
.9846
.9850
.9854
.9887
.9913
.9857
2.2
.9861
.9864
.9868
.9871
.9875
.9878
.9881
.9884
.9890
2.3
.9893
.9896
.9898
.9901
.9904
.9906
.9909
.9911
.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
.9953
.9955
.9956
.9957
.9959
.9960
.9961
.9962
.9963
.9964
2.7
.9965
.9966
.9967
.9968
.9969
.9970
.9971
.9972
.9973
.9974
.9977
.9983
2.8
.9974
.9975
.9976
.9977
.9978
.9979
.9979
.9980
.9981
2.9
.9981
.9982
.9982
.9984
.9984
.9985
.9985
9986
.9986
3.0
.9987
.9987
.9987
.9988
9988
.9989
.9989
.9989
.9990
.9990
3.1
.9990
.9991
.9991
.9991
.9992
.9992
.9992
.9992
.9993
.9993
3.2
.9993
.9993
.9994
.9994
.9994
.9994
.9994
.9996
.9995
.9995
.9995
3.3
.9995
.9995
.9995
.9996
.9996
.9996
.9996
.9996
.9997
3.4
.9997
.9997
.9997
.9997
.9997
.9997
.9997
.9997
.9997
.9998

Expert Solution

Step 1

Quartiles: The observations Q_1, Q_2, And Q₃ which divide the total number of observations into 4 equal parts are called Quartiles

Given,

Population mean = $μ = 500$

Population standard deviation = $σ$ = 10.6

$x ~ N (500, 10.6)$

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