The acceptable level for insect filth in a certain food item is 4 insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A simple random sample of 40 ten-gram portions of the food item is obtained and results in a sample mean of x = 4.2 insect fragments per ten-gram portion. Complete parts (a) through (c) below. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) Why is the sampling distribution of x approximately normal? O A. The sampling distribution is approximately normal because the popluation is normally distributed. O B. The sampling distribution is assumed to be approximately normal. O C. The sampling distribution is approximately normal because the sample size is large enough. D. The sampling distribution is approximately normal because the population is normally distributed and the sample size is large enough.

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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The acceptable level for insect filth in a certain food item is 4 insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A simple random sample of 40
ten-gram portions of the food item is obtained and results in a sample mean of x = 4.2 insect fragments per ten-gram portion. Complete parts (a) through (c) below.
Click here to view the standard normal distribution table (page 1).
Click here to view the standard normal distribution table (page 2).
(a) Why is the sampling distribution of x approximately normal?
OA. The sampling distribution is approximately normal because the popluation is normally distributed.
O B. The sampling distribution is assumed to be approximately normal.
OC. The sampling distribution is approximately normal because the sample size is large enough.
O D. The sampling distribution is approximately normal because the population is normally distributed and the sample size is large enough.
O Standard Normal Distribution Table (page 1)
Area
Standard Normal Distribution
0.00
0.01
0.02
0.03
0.04
0.05
0,06
0.07
0,08
0,09
-34
0.0003
0.0005
0.0007
0.0010
0.0013
0.0003
0.0005
0.0007
0.0003
0.0005
0.0006
0.0003
0.0004
0.0003
0.0004
0.0006
0.0003
0.0004
0.0006
0.0003
0.0004
0.0006
0.0003
0.0004
0.0005
0.0003
0.0004
0.0005
0.0002
0.0003
0.0005
0.0007
0.0010
-32
0.0006
0.0009
-31
-30
0.0008
0.0012
0.0008
0.0011
0.0007
0.0010
0.0009
0.0009
0.0008
0.0011
0.0008
0.0013
0.0013
0.0012
0.0011
0.0014
0.0019
0.0026
0.0036
0.0015
-29
-28
-2.7
0.0019
0.0026
0.0035
0.0018
0.0025
0.0034
0.0018
0.0024
0.0033
0.0017
0.0023
0.0032
0.0016
0.0023
0.0031
0.0016
0.0022
0.0021
0.0029
0.0015
0.0021
0.0028
0.0014
0.0020
0.0027
-26
-2.5
0.0047
0.0062
0.0045
0.0060
0.0044
0.0059
0.0043
0.0057
0.0030
0.0040
0.0054
0.0039
0.0052
0.0038
0.0051
0.0041
0.0037
0.0049
0.0055
0.0048
-24
-23
-2.2
-2.1
-2.0
0.0082
0.0107
0.0139
0.0179
0.0228
0.0080
0.0078
0.0075
0.0099
0.0073
0.0096
0.0071
0.0069
0.0068
0.0089
0.0066
0.0064
0.0104
0.0136
0.0174
0.0222
0.0102
0.0132
0.0170
0.0217
0.0094
0.0122
0.0158
0.0202
0.0091
0.0119
0.0154
0.0197
0.0087
0.0113
0.0146
0.0188
0.0084
0.0110
0.0129
0.0166
0.0212
0.0125
0.0162
0.0207
0.0116
0.0150
0.0192
0.0143
0.0183
-1.9
-1.K
-1.7
0.0287
0.0359
0.0446
0.0548
0.0668
0.0281
0.0351
0.0436
0.0537
0.0655
0.0274
0,0344
0.0427
0.0526
0.0643
0.0268
0.0336
0.0418
0.0516
0.0630
0.0262
0.0256
0.0322
0.0401
0.0495
0.0606
0.0250
0.0314
0.0392
0.0244
0.0307
0.0239
0.0301
0.0375
0.0465
0.0233
0.0294
0.0367
0.0329
0.0400
0.0384
0.0475
-16
0.0505
0.0618
0.0485
0.0455
0.0559
-1.5
0.0594
0.0582
0.0571
0.0793
0.0951
0.1131
0.1335
0.1562
0.0778
0.0934
0.1112
0.0764
-14
-1.3
-1.2
0.0808
0.0968
0.1151
0.1357
0.1587
0.0918
0.1093
0.1292
0.1515
0.0749
0.0901
0.1075
0.0735
0.0885
0.1056
0.1251
0.1469
0.0721
0.0869
0.1038
0.1230
0.1446
0.0708
0.0853
0.1020
0.1210
0.1423
0.0694
0.0838
0.1003
0.0681
0.0823
0.0985
0.1170
0.1379
-1.1
-1.0
0.1314
0.1539
0.1271
0.1492
0.1190
0.1401
-0.9
0.1841
0.1814
0.2090
0.2389
0.2709
0.3050
0.1788
0.1762
0.2033
0.2327
0.2643
0.2981
0.1736
0.1711
0.1685
0.1949
0.1660
0.1635
0.1894
0.2177
0.2483
0.2810
0.1611
0.1867
02119
02420
02743
0.3085
0.2061
0.2358
0.2676
0.3015
0.2005
0.2296
0.2611
0.2946
0.1977
0.2266
0.2578
0.2912
0.1922
0.2206
0.2514
0.2843
-07
0.2236
0.2546
0.2877
0.2148
0.2451
0.2776
-0.5
0.3409
0.3783
04168
0.3372
0.3745
0.4129
0.4522
0.4920
03336
03707
0.4090
0.3300
0.3669
0.4052
0.4443
0.4840
0.3264
0.3632
0.4013
0.3228
0.3594
0.3974
0.3121
0.3483
0.3859
-04
-0.3
0.3446
0.3821
0.3192
0.3557
0.3936
0.3156
0.3520
0.3897
-0.2
-0.1
04207
0.4602
0.5000
04562
0.4960
0.4483
0.4880
0.4404
0.4801
0.4364
0.4761
0.4325
04286
0.4681
0.4247
0.4641
0.4721
0,00
0.01
0.02
0.03
0.04
0.05
0.06
0,07
0.08
0.09
Transcribed Image Text:The acceptable level for insect filth in a certain food item is 4 insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A simple random sample of 40 ten-gram portions of the food item is obtained and results in a sample mean of x = 4.2 insect fragments per ten-gram portion. Complete parts (a) through (c) below. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) Why is the sampling distribution of x approximately normal? OA. The sampling distribution is approximately normal because the popluation is normally distributed. O B. The sampling distribution is assumed to be approximately normal. OC. The sampling distribution is approximately normal because the sample size is large enough. O D. The sampling distribution is approximately normal because the population is normally distributed and the sample size is large enough. O Standard Normal Distribution Table (page 1) Area Standard Normal Distribution 0.00 0.01 0.02 0.03 0.04 0.05 0,06 0.07 0,08 0,09 -34 0.0003 0.0005 0.0007 0.0010 0.0013 0.0003 0.0005 0.0007 0.0003 0.0005 0.0006 0.0003 0.0004 0.0003 0.0004 0.0006 0.0003 0.0004 0.0006 0.0003 0.0004 0.0006 0.0003 0.0004 0.0005 0.0003 0.0004 0.0005 0.0002 0.0003 0.0005 0.0007 0.0010 -32 0.0006 0.0009 -31 -30 0.0008 0.0012 0.0008 0.0011 0.0007 0.0010 0.0009 0.0009 0.0008 0.0011 0.0008 0.0013 0.0013 0.0012 0.0011 0.0014 0.0019 0.0026 0.0036 0.0015 -29 -28 -2.7 0.0019 0.0026 0.0035 0.0018 0.0025 0.0034 0.0018 0.0024 0.0033 0.0017 0.0023 0.0032 0.0016 0.0023 0.0031 0.0016 0.0022 0.0021 0.0029 0.0015 0.0021 0.0028 0.0014 0.0020 0.0027 -26 -2.5 0.0047 0.0062 0.0045 0.0060 0.0044 0.0059 0.0043 0.0057 0.0030 0.0040 0.0054 0.0039 0.0052 0.0038 0.0051 0.0041 0.0037 0.0049 0.0055 0.0048 -24 -23 -2.2 -2.1 -2.0 0.0082 0.0107 0.0139 0.0179 0.0228 0.0080 0.0078 0.0075 0.0099 0.0073 0.0096 0.0071 0.0069 0.0068 0.0089 0.0066 0.0064 0.0104 0.0136 0.0174 0.0222 0.0102 0.0132 0.0170 0.0217 0.0094 0.0122 0.0158 0.0202 0.0091 0.0119 0.0154 0.0197 0.0087 0.0113 0.0146 0.0188 0.0084 0.0110 0.0129 0.0166 0.0212 0.0125 0.0162 0.0207 0.0116 0.0150 0.0192 0.0143 0.0183 -1.9 -1.K -1.7 0.0287 0.0359 0.0446 0.0548 0.0668 0.0281 0.0351 0.0436 0.0537 0.0655 0.0274 0,0344 0.0427 0.0526 0.0643 0.0268 0.0336 0.0418 0.0516 0.0630 0.0262 0.0256 0.0322 0.0401 0.0495 0.0606 0.0250 0.0314 0.0392 0.0244 0.0307 0.0239 0.0301 0.0375 0.0465 0.0233 0.0294 0.0367 0.0329 0.0400 0.0384 0.0475 -16 0.0505 0.0618 0.0485 0.0455 0.0559 -1.5 0.0594 0.0582 0.0571 0.0793 0.0951 0.1131 0.1335 0.1562 0.0778 0.0934 0.1112 0.0764 -14 -1.3 -1.2 0.0808 0.0968 0.1151 0.1357 0.1587 0.0918 0.1093 0.1292 0.1515 0.0749 0.0901 0.1075 0.0735 0.0885 0.1056 0.1251 0.1469 0.0721 0.0869 0.1038 0.1230 0.1446 0.0708 0.0853 0.1020 0.1210 0.1423 0.0694 0.0838 0.1003 0.0681 0.0823 0.0985 0.1170 0.1379 -1.1 -1.0 0.1314 0.1539 0.1271 0.1492 0.1190 0.1401 -0.9 0.1841 0.1814 0.2090 0.2389 0.2709 0.3050 0.1788 0.1762 0.2033 0.2327 0.2643 0.2981 0.1736 0.1711 0.1685 0.1949 0.1660 0.1635 0.1894 0.2177 0.2483 0.2810 0.1611 0.1867 02119 02420 02743 0.3085 0.2061 0.2358 0.2676 0.3015 0.2005 0.2296 0.2611 0.2946 0.1977 0.2266 0.2578 0.2912 0.1922 0.2206 0.2514 0.2843 -07 0.2236 0.2546 0.2877 0.2148 0.2451 0.2776 -0.5 0.3409 0.3783 04168 0.3372 0.3745 0.4129 0.4522 0.4920 03336 03707 0.4090 0.3300 0.3669 0.4052 0.4443 0.4840 0.3264 0.3632 0.4013 0.3228 0.3594 0.3974 0.3121 0.3483 0.3859 -04 -0.3 0.3446 0.3821 0.3192 0.3557 0.3936 0.3156 0.3520 0.3897 -0.2 -0.1 04207 0.4602 0.5000 04562 0.4960 0.4483 0.4880 0.4404 0.4801 0.4364 0.4761 0.4325 04286 0.4681 0.4247 0.4641 0.4721 0,00 0.01 0.02 0.03 0.04 0.05 0.06 0,07 0.08 0.09
Standard Normal Distribution Table (page 2)
Area -
Standard Normal Distribution
0.00
0,01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.0
0.1
0.2
0.5000
0.5398
0.5793
0.6179
0.6554
0.5040
0.5438
0.5832
0.6217
0.6591
0.5080
0.5478
0.5871
0.6255
0.6628
0.5120
0,5517
0.5910
0.5160
0.5557
0.5948
0.5199
0.5596
0.5987
0.5239
0,5636
0.6026
0.6406
0.6772
0.5279
0.5675
0.6064
0.6443
0.6808
0.5319
0.5714
0.6103
0,6480
0,6844
0,5359
0.5753
0.6141
0,6517
0,6879
0.6293
0.6664
0.6331
0.6700
0.6368
0.6736
0.3
0.4
0.6915
0.7257
0.7580
0.7881
0.8159
0.6985
0.7324
0.7642
0.7939
0.8212
0.7088
0.7422
0.7734
0.7123
0.7454
0.7764
0.5
0.7157
0.6950
0.7291
0.7611
0.7019
0.7357
0.7673
0.7967
0.8238
0.7054
0.7389
0.7704
0.7190
0,7517
0.7823
0,7224
0,7549
0.6
0.7486
0.7794
0,8078
0.7852
0.8133
0.8389
0,7
0.7910
0.8186
0.8023
0.8289
0.8051
0.8315
0.8106
0.8365
0.8
0.7995
0.8264
0.9
0.8340
0.8531
0,8749
0.8944
0.9115
0.9265
0.8413
0.8643
0.8461
0.8485
0.8708
0.8907
0.9082
0.9236
0.8508
0.8729
0.8925
0.8577
0.8790
0.8599
0,8810
0.8997
0.9162
0.9306
0.8621
1.0
1.1
1.2
0.8438
0.8665
0.8869
0.9049
0.9207
0.8554
0,8770
0.8962
0.9131
0.9279
0.8686
0.8849
0.9032
0.9192
0.8888
0.9066
0.9222
0.8830
0,90 15
0.9177
0.9319
0.8980
1.3
1.4
0.9099
0.9251
0.9147
0.9292
1.5
1.6
1.7
0.9332
0.9452
0.9554
0.9641
0.9713
0.9345
0.9463
0.9564
0.9649
0.9719
0.9357
0.9474
0.9573
0.9656
0.9726
0.9370
0.9484
0.9582
0.9664
0.9732
0.9382
0.9495
0.9591
0.9394
0.9505
0.9599
0.9678
0.9744
0.9406
0.9515
0.9608
0.9686
0.9750
0.9418
0.9525
0.9616
0.9429
0.9535
0.9625
0.9699
0.9761
0.9441
0.9545
0.9633
0.9706
0.9767
0.9671
0.9738
0.9693
0.9756
1.8
1.9
2.0
2.1
2.2
2.3
2.4
0.9772
0.9821
0.9861
0.9893
0,9918
0.9778
0.9826
0,9864
0.9896
0.9920
0.9783
0.9830
0.9868
0,9788
0.9834
0.9871
0.9901
0.9925
0.9793
0.9838
0.9875
0.9904
0.9927
0.9798
0.9842
0.9878
0.9803
0.9846
0.9881
0.9808
0.9850
0.9884
0,9812
0.9854
0.9887
0.9913
0.9934
0.9817
0.9857
0.9890
0.9916
0.9936
0.9898
0.9906
0.9909
0.9911
0.9922
0.9929
0.9931
0.9932
0.9945
0.9959
0.9969
2.5
2.6
2.7
2.8
0.9938
0.9953
0.9965
0.9974
0.9981
0.9940
0.9955
0.9966
0.9941
0.9956
0.9967
0.9976
0.9982
0.9943
0.9957
0.9968
0.9946
0.9960
0,9970
0.9978
0.9984
0.9948
0.9961
0.9971
0.9949
0.9962
0.9972
0.9951
0.9963
0.9973
0.9980
0.9986
0.9952
0.9964
0.9974
0.9975
0.9982
0.9977
0.9983
0.9977
0.9984
0.9979
0.9985
0.9979
0.9985
0.9981
0.9986
2.9
0.9990
0.9993
0.9995
0,9997
0,9987
0.9989
0.9992
0.9994
0,9996
0.9997
0.9989
0.9992
0.9994
3.0
3.1
0.9990
0.9993
0.9995
0.9987
0.9991
0.9993
0,9995
0.9997
0.9987
0.9991
0.9994
0.9988
0.9991
0.9994
0,9996
0.9988
0.9992
0.9994
0.9996
0.9997
0.9989
0.9992
0.9995
0.9996
0,9997
0.9990
0.9993
0.9995
3.2
3.3
3.4
0,9996
0.9997
0.9996
0.9995
0.9997
0.9997
0.9997
0.9997
0.9998
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
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Transcribed Image Text:Standard Normal Distribution Table (page 2) Area - Standard Normal Distribution 0.00 0,01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.1 0.2 0.5000 0.5398 0.5793 0.6179 0.6554 0.5040 0.5438 0.5832 0.6217 0.6591 0.5080 0.5478 0.5871 0.6255 0.6628 0.5120 0,5517 0.5910 0.5160 0.5557 0.5948 0.5199 0.5596 0.5987 0.5239 0,5636 0.6026 0.6406 0.6772 0.5279 0.5675 0.6064 0.6443 0.6808 0.5319 0.5714 0.6103 0,6480 0,6844 0,5359 0.5753 0.6141 0,6517 0,6879 0.6293 0.6664 0.6331 0.6700 0.6368 0.6736 0.3 0.4 0.6915 0.7257 0.7580 0.7881 0.8159 0.6985 0.7324 0.7642 0.7939 0.8212 0.7088 0.7422 0.7734 0.7123 0.7454 0.7764 0.5 0.7157 0.6950 0.7291 0.7611 0.7019 0.7357 0.7673 0.7967 0.8238 0.7054 0.7389 0.7704 0.7190 0,7517 0.7823 0,7224 0,7549 0.6 0.7486 0.7794 0,8078 0.7852 0.8133 0.8389 0,7 0.7910 0.8186 0.8023 0.8289 0.8051 0.8315 0.8106 0.8365 0.8 0.7995 0.8264 0.9 0.8340 0.8531 0,8749 0.8944 0.9115 0.9265 0.8413 0.8643 0.8461 0.8485 0.8708 0.8907 0.9082 0.9236 0.8508 0.8729 0.8925 0.8577 0.8790 0.8599 0,8810 0.8997 0.9162 0.9306 0.8621 1.0 1.1 1.2 0.8438 0.8665 0.8869 0.9049 0.9207 0.8554 0,8770 0.8962 0.9131 0.9279 0.8686 0.8849 0.9032 0.9192 0.8888 0.9066 0.9222 0.8830 0,90 15 0.9177 0.9319 0.8980 1.3 1.4 0.9099 0.9251 0.9147 0.9292 1.5 1.6 1.7 0.9332 0.9452 0.9554 0.9641 0.9713 0.9345 0.9463 0.9564 0.9649 0.9719 0.9357 0.9474 0.9573 0.9656 0.9726 0.9370 0.9484 0.9582 0.9664 0.9732 0.9382 0.9495 0.9591 0.9394 0.9505 0.9599 0.9678 0.9744 0.9406 0.9515 0.9608 0.9686 0.9750 0.9418 0.9525 0.9616 0.9429 0.9535 0.9625 0.9699 0.9761 0.9441 0.9545 0.9633 0.9706 0.9767 0.9671 0.9738 0.9693 0.9756 1.8 1.9 2.0 2.1 2.2 2.3 2.4 0.9772 0.9821 0.9861 0.9893 0,9918 0.9778 0.9826 0,9864 0.9896 0.9920 0.9783 0.9830 0.9868 0,9788 0.9834 0.9871 0.9901 0.9925 0.9793 0.9838 0.9875 0.9904 0.9927 0.9798 0.9842 0.9878 0.9803 0.9846 0.9881 0.9808 0.9850 0.9884 0,9812 0.9854 0.9887 0.9913 0.9934 0.9817 0.9857 0.9890 0.9916 0.9936 0.9898 0.9906 0.9909 0.9911 0.9922 0.9929 0.9931 0.9932 0.9945 0.9959 0.9969 2.5 2.6 2.7 2.8 0.9938 0.9953 0.9965 0.9974 0.9981 0.9940 0.9955 0.9966 0.9941 0.9956 0.9967 0.9976 0.9982 0.9943 0.9957 0.9968 0.9946 0.9960 0,9970 0.9978 0.9984 0.9948 0.9961 0.9971 0.9949 0.9962 0.9972 0.9951 0.9963 0.9973 0.9980 0.9986 0.9952 0.9964 0.9974 0.9975 0.9982 0.9977 0.9983 0.9977 0.9984 0.9979 0.9985 0.9979 0.9985 0.9981 0.9986 2.9 0.9990 0.9993 0.9995 0,9997 0,9987 0.9989 0.9992 0.9994 0,9996 0.9997 0.9989 0.9992 0.9994 3.0 3.1 0.9990 0.9993 0.9995 0.9987 0.9991 0.9993 0,9995 0.9997 0.9987 0.9991 0.9994 0.9988 0.9991 0.9994 0,9996 0.9988 0.9992 0.9994 0.9996 0.9997 0.9989 0.9992 0.9995 0.9996 0,9997 0.9990 0.9993 0.9995 3.2 3.3 3.4 0,9996 0.9997 0.9996 0.9995 0.9997 0.9997 0.9997 0.9997 0.9998 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 Print Done
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