1) The red blood cell count for a population of adult males can be approximated by a normaldistribution, with a mean of 5.4 million cells per microliter and a standard deviation of 0.4 millioncells per microliter. What is the minimum red blood cell count that can be in the top 25% ofcounts? What is the maximum red blood cell count that can be in the bottom 15% of counts? 2) A vending machine dispenses coffee into an 8-ounce cup. The amounts of coffee dispensed intothe cup are normally distributed, with a standard deviation of 0.03 ounces. You can allow the cupto overflow 1% of the time. What amount should you set as the mean amount of coffee to bedispensed? 3) A large population has a mean of 310 and a standard deviation of 37. Draw out a normal curveand label the values at 1, 2, and 3 standard deviations away from the mean. Then, using theempirical rule, find what percentage of the observations fall in the intervals μ ± 1ơ, μ ± 2ơ, andμ ± 3ơ. Table A (Continued)2.32.42.52.61.61.71.81.92.02.12.22.72.82.93.03.13.2Table entry for z is theprobability lying below z.0.50.60.70.80.91.01.11.21.31.41.53.33.4Z0.00.10.20.30.4.00.50005398.5793.6179.6554.6915.7257.7580.7881.8159.8413.8643.8849.9032.9192.9332.9452.95549641.9713.9772.9821.9861.9893.9918.9938.9953.9965.9974.9981.9987.9990.9993.9995.9997.01.5040.5438.5832.6217.6591.6950.7291.7611.7910.8186.8438.8665.8869.9049.9207.9345.9463.9564.96499719.9778.9826.9864.9896.9920.9940.9955.9966.9975.9982.9987.9991.9993.9995.9997.02.5080.5478.5871.6255.6628.6985.7324.7642.7939.8212.8461.8686.8888.9066.9222.9357.9474.9573.9656.9726.9783.9830.9868.9898.9922.9941..9956.9967.9976.9982.9987.9991.9994.9995.9997.03.5120.5517.5910.6293.6664.7019.7357.7673.7967.8238.8485.8708.8907.9082.9236.9370.9484.9582.9664.9732.9788.9834.9871.9901.9925.9943.9957.9968.9977.9983.9988.9991.9994.9996.9997Probability.04.5160.5557.5948.6331.6700.7054.7389.77047995.8264.8508.8729.8925.9099.9251.9382.9495.9591.9671.9738.9793.9838.9875.99049927.9945.9959.9969.9977.9984.9988.9992.9994.9996.9997.05.5199.5596.5987.6368.6736.7088.7422.7734.8023.8289.8531.8749.8944.9115.9265.9394.9505.9599.9678.9744.9798.9842.9878.9906.9929.99469960.9970.9978.9984.9989.9992.99949996.9997.06.5239.5636.6026.6406.6772.7123.7454.7764.8051.8315.8554.8770.8962.9131.9279.9406.9515.9608.9686.9750.9803.9846.98819909.99319948.9961.9971.9979.99859989.99929994.9996.99972.07.5279.5675.6064.6443.6808.7157.7486.7794.8078.8340.8577.8790.8980.9147.9292.9418.9525.9616.9693.97569808.9850.9884.9911.99329949.99629972.08.5319.5714.6103.6480.6844.7190.7517.7823.8106.8365.8599.8810.8997.9162.9306.9429.9535.9625.9699.97619812.98549887991399169934 ..9936.9951.9952.9963.9964.9973.9974.9980.9981.99869986.9990.9990.9993.9993.9995.9995.9996.9997.99979998.09.5359.5753.6141.9979.9985.9989.9992.9995.9996.9997.6517.6879.7224.7549.7852.8133.8389.8621.8830.90159177.931994419545.9633.9706.97679817.9857.9890 Table A Standard normal probabilitiesZ-3.4-3.3-3.2-3.1-3.0-2.9-2.8-2.7-2.6-2.5-2.4-2.3-2.2-2.1-2.0-1.9- 1.8-1.7-1.6-1.5-1.4-1.3- 1.2- 1.1-1.0-0.9-0.8-0.7-0.6-0.5Table entry for z is theprobability lying below z.-0.4-0.3-0.2-0.1-0.0.00.0003.0005,0007.0010.0013.0019.0026.0035.0047.0062.0082.0107.0139.0179.0228.0287.0359.0446.0548.0668.0808.0968.1151.1357.1587.1841.2119.2420.2743.3085.3446.3821.4207.4602.5000.01.0003.0005.0007.0009.0013.0018.0025.0034.0045.0060.0080.0104.0136.0174.0222,0281.0351.0436.0537.0655.0793.0951.1131.1335.1562.1814.2090.2389.2709.3050.3409.3783.4168.4562.4960.02.0003.0005.0006.0009.0013.0018.0024.0033.0044.0059.0078.0102.0132.0170.0217.0274.0344.0427.0526.0643.0778.09341112.1314.1539.1788.2061.2358.2676.3015.3372.3745.4129.4522.4920Probability.03.0003.0004.0006.0009.0012.0017.0023.0032.0043.0057.0075.0099.0129.0166.0212.0268.0336.0418.0516.0630.0764.0918.1093.1292.1515.1762.2033.2327.2643.2981.3336.3707.4090.4483.4880.04.0003.0004.0006.0008.0012.0016.0023.0031.0041.0055.0073.0096.0125.0162.0207.0262.0329.04090505.0618.0749.0901.1075.1271.1492.1736.2005.2296.2611.2946.3300.3669.4052.4443.4840Z.05.0003.0004.0006.0008.0011.0016.0022.0030.0040.0054.0071.00940122.0158.0202.0256.0322.04010495.0606.0735.0885.1056.1251.1469.1711.19772266.25782912.3264.3632.4013.4404.4801.06.0003.0004.0006.0008.0011.0015.0021.0029.0039.0052.0069.0091.0119.0154.0197.0250.0314.0392.0485.0594.0721.0869.1038.1230.14461685.1949.2236.25462877.32283594.3974.43644761.070.0003.0004.0005.0008.0011.0015.0021.0028.0038.0051.0068.0089.0116.0150.0192.0244.0307.0384.0475.0582.07080853.1020.1210.14231660.1922.2206.2514.2843.3192.3557.3936.4325.4721.08.0003.0004.0005.0007.0010.0014.0020.0027.0037.0049.0066.0087.01130146.0188.0239.0301.037504650571.0694.09.0002.00030005.0007.0010.0014.0019.0026.0036.0048.0064.0084.01100143.01830233.0838.10031190.1401.1635.1894.0294.03670455.0559.0681.0823.0985.1170.1379.1611.186721772148.2483 .24512810.2776.315631213520.3483.3897.3859.42864247.4681.4641

Given Information: The mean of the distribution, μ=5.4 The standard deviation of the observation,…

Answered: 1) The red blood cell count for a…

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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Related questions

Question

1) The red blood cell count for a population of adult males can be approximated by a normal
distribution, with a mean of 5.4 million cells per microliter and a standard deviation of 0.4 million
cells per microliter. What is the minimum red blood cell count that can be in the top 25% of
counts? What is the maximum red blood cell count that can be in the bottom 15% of counts?

2) A vending machine dispenses coffee into an 8-ounce cup. The amounts of coffee dispensed into
the cup are normally distributed, with a standard deviation of 0.03 ounces. You can allow the cup
to overflow 1% of the time. What amount should you set as the mean amount of coffee to be
dispensed?

3) A large population has a mean of 310 and a standard deviation of 37. Draw out a normal curve
and label the values at 1, 2, and 3 standard deviations away from the mean. Then, using the
empirical rule, find what percentage of the observations fall in the intervals μ ± 1ơ, μ ± 2ơ, and
μ ± 3ơ.

Table A (Continued)
2.3
2.4
2.5
2.6
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.7
2.8
2.9
3.0
3.1
3.2
Table entry for z is the
probability lying below z.
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
3.3
3.4
Z
0.0
0.1
0.2
0.3
0.4
.00
.5000
5398
.5793
.6179
.6554
.6915
.7257
.7580
.7881
.8159
.8413
.8643
.8849
.9032
.9192
.9332
.9452
.9554
9641
.9713
.9772
.9821
.9861
.9893
.9918
.9938
.9953
.9965
.9974
.9981
.9987
.9990
.9993
.9995
.9997
.01
.5040
.5438
.5832
.6217
.6591
.6950
.7291
.7611
.7910
.8186
.8438
.8665
.8869
.9049
.9207
.9345
.9463
.9564
.9649
9719
.9778
.9826
.9864
.9896
.9920
.9940
.9955
.9966
.9975
.9982
.9987
.9991
.9993
.9995
.9997
.02
.5080
.5478
.5871
.6255
.6628
.6985
.7324
.7642
.7939
.8212
.8461
.8686
.8888
.9066
.9222
.9357
.9474
.9573
.9656
.9726
.9783
.9830
.9868
.9898
.9922
.9941.
.9956
.9967
.9976
.9982
.9987
.9991
.9994
.9995
.9997
.03
.5120
.5517
.5910
.6293
.6664
.7019
.7357
.7673
.7967
.8238
.8485
.8708
.8907
.9082
.9236
.9370
.9484
.9582
.9664
.9732
.9788
.9834
.9871
.9901
.9925
.9943
.9957
.9968
.9977
.9983
.9988
.9991
.9994
.9996
.9997
Probability
.04
.5160
.5557
.5948
.6331
.6700
.7054
.7389
.7704
7995
.8264
.8508
.8729
.8925
.9099
.9251
.9382
.9495
.9591
.9671
.9738
.9793
.9838
.9875
.9904
9927
.9945
.9959
.9969
.9977
.9984
.9988
.9992
.9994
.9996
.9997
.05
.5199
.5596
.5987
.6368
.6736
.7088
.7422
.7734
.8023
.8289
.8531
.8749
.8944
.9115
.9265
.9394
.9505
.9599
.9678
.9744
.9798
.9842
.9878
.9906
.9929
.9946
9960
.9970
.9978
.9984
.9989
.9992
.9994
9996
.9997
.06
.5239
.5636
.6026
.6406
.6772
.7123
.7454
.7764
.8051
.8315
.8554
.8770
.8962
.9131
.9279
.9406
.9515
.9608
.9686
.9750
.9803
.9846
.9881
9909
.9931
9948
.9961
.9971
.9979
.9985
9989
.9992
9994
.9996
.9997
2
.07
.5279
.5675
.6064
.6443
.6808
.7157
.7486
.7794
.8078
.8340
.8577
.8790
.8980
.9147
.9292
.9418
.9525
.9616
.9693
.9756
9808
.9850
.9884
.9911
.9932
9949
.9962
9972
.08
.5319
.5714
.6103
.6480
.6844
.7190
.7517
.7823
.8106
.8365
.8599
.8810
.8997
.9162
.9306
.9429
.9535
.9625
.9699
.9761
9812
.9854
9887
9913
9916
9934 ..9936
.9951
.9952
.9963
.9964
.9973
.9974
.9980
.9981
.9986
9986
.9990
.9990
.9993
.9993
.9995
.9995
.9996
.9997
.9997
9998
.09
.5359
.5753
.6141
.9979
.9985
.9989
.9992
.9995
.9996
.9997
.6517
.6879
.7224
.7549
.7852
.8133
.8389
.8621
.8830
.9015
9177
.9319
9441
9545
.9633
.9706
.9767
9817
.9857
.9890

Table A Standard normal probabilities
Z
-3.4
-3.3
-3.2
-3.1
-3.0
-2.9
-2.8
-2.7
-2.6
-2.5
-2.4
-2.3
-2.2
-2.1
-2.0
-1.9
- 1.8
-1.7
-1.6
-1.5
-1.4
-1.3
- 1.2
- 1.1
-1.0
-0.9
-0.8
-0.7
-0.6
-0.5
Table entry for z is the
probability lying below z.
-0.4
-0.3
-0.2
-0.1
-0.0
.00
.0003
.0005
,0007
.0010
.0013
.0019
.0026
.0035
.0047
.0062
.0082
.0107
.0139
.0179
.0228
.0287
.0359
.0446
.0548
.0668
.0808
.0968
.1151
.1357
.1587
.1841
.2119
.2420
.2743
.3085
.3446
.3821
.4207
.4602
.5000
.01
.0003
.0005
.0007
.0009
.0013
.0018
.0025
.0034
.0045
.0060
.0080
.0104
.0136
.0174
.0222
,0281
.0351
.0436
.0537
.0655
.0793
.0951
.1131
.1335
.1562
.1814
.2090
.2389
.2709
.3050
.3409
.3783
.4168
.4562
.4960
.02
.0003
.0005
.0006
.0009
.0013
.0018
.0024
.0033
.0044
.0059
.0078
.0102
.0132
.0170
.0217
.0274
.0344
.0427
.0526
.0643
.0778
.0934
1112
.1314
.1539
.1788
.2061
.2358
.2676
.3015
.3372
.3745
.4129
.4522
.4920
Probability
.03
.0003
.0004
.0006
.0009
.0012
.0017
.0023
.0032
.0043
.0057
.0075
.0099
.0129
.0166
.0212
.0268
.0336
.0418
.0516
.0630
.0764
.0918
.1093
.1292
.1515
.1762
.2033
.2327
.2643
.2981
.3336
.3707
.4090
.4483
.4880
.04
.0003
.0004
.0006
.0008
.0012
.0016
.0023
.0031
.0041
.0055
.0073
.0096
.0125
.0162
.0207
.0262
.0329
.0409
0505
.0618
.0749
.0901
.1075
.1271
.1492
.1736
.2005
.2296
.2611
.2946
.3300
.3669
.4052
.4443
.4840
Z
.05
.0003
.0004
.0006
.0008
.0011
.0016
.0022
.0030
.0040
.0054
.0071
.0094
0122
.0158
.0202
.0256
.0322
.0401
0495
.0606
.0735
.0885
.1056
.1251
.1469
.1711
.1977
2266
.2578
2912
.3264
.3632
.4013
.4404
.4801
.06
.0003
.0004
.0006
.0008
.0011
.0015
.0021
.0029
.0039
.0052
.0069
.0091
.0119
.0154
.0197
.0250
.0314
.0392
.0485
.0594
.0721
.0869
.1038
.1230
.1446
1685
.1949
.2236
.2546
2877
.3228
3594
.3974
.4364
4761
.07
0.0003
.0004
.0005
.0008
.0011
.0015
.0021
.0028
.0038
.0051
.0068
.0089
.0116
.0150
.0192
.0244
.0307
.0384
.0475
.0582
.0708
0853
.1020
.1210
.1423
1660
.1922
.2206
.2514
.2843
.3192
.3557
.3936
.4325
.4721
.08
.0003
.0004
.0005
.0007
.0010
.0014
.0020
.0027
.0037
.0049
.0066
.0087
.0113
0146
.0188
.0239
.0301
.0375
0465
0571
.0694
.09
.0002
.0003
0005
.0007
.0010
.0014
.0019
.0026
.0036
.0048
.0064
.0084
.0110
0143
.0183
0233
.0838
.1003
1190
.1401
.1635
.1894
.0294
.0367
0455
.0559
.0681
.0823
.0985
.1170
.1379
.1611
.1867
2177
2148
.2483 .2451
2810
.2776
.3156
3121
3520
.3483
.3897
.3859
.4286
4247
.4681
.4641

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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