The caffeine content (in mg) was examined for a random sample of 50 cups of black coffee dispensed by a new machine. The mean and standard deviation were 110 mg and 7.1 mg respectively. Use the data to construct a 98% confidence interval for the mean caffeine content for cups dispensed by the machine.

Question
Asked Oct 28, 2019

The caffeine content (in mg) was examined for a random sample of 50 cups of black coffee dispensed by a new machine. The mean and standard deviation were 110 mg and 7.1 mg respectively. Use the data to construct a 98% confidence interval for the mean caffeine content for cups dispensed by the machine. 

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Step 1

Given sample size of black coffee cups n = 50
Caffeine content mean = 110mg
Standard deviation = 7.1 mg

The Z score for 98% confidence interval will have 0.9...

0.06
0.07
0.08
0.09
0.0
0.01
0.02
0.03
0.04
0.05
0.5000
0.5040
0.5080
0.5120
0.5160
0.5199
0.5239
0.5279
0.5319
0.5359
0.0
0.5596
0.5987
0.5398
0.5636
0.1
0.5438
0.5478
0.5517
0.5557
0.5675
0.5714
0.5753
0.2
0.5871
0.5948
0.5793
0.5832
0.5910
0.6026
0.6064
0.6103
0.6141
0.6331
0.6368
0.6443
0.3
0.6179
0.6217
0.6255
0.6293
0.6406
0.6480
0.6517
0.6554
0.6664
0.6736
0.4
0.6591
0.6628
0.6700
0.6772
0.6808
0.6844
0.6879
0.5
0.6915
0.6950
0.6985
0.7019
0.7054
0.7088
0.7123
0.7157
0.7190
0.7224
0.7257
0.7580
0.7357
0.7422
0.6
0.7291
0.7324
0.7389
0.7454
0.7486
0.7517
0.7549
0.7611
0.7852
0.7642
0.7673
0.7704
0.7734
0.7764
0.7794
0.7823
0.7
0.8023
0.7881
0.7910
0.7939
0.7967
0.7995
0.8051
0.8078
0.8106
0.8133
0.8
98%
0.8389
0.9
0.8159
0.8186
0.8212
0.8238
0.8264
0.8289
0.8315
0.8340
0.8365
0.8508
0.8554
0.8577
1.0
0.8413
0.8438
0.8461
0.8485
0.8531
0.8599
0.8621
0.8643
0.8686
0.8729
1.1
0.8665
0.8708
0.8749
0.8770
0.8790
0.8810
0.8830
1%
0.8997
1.2
0.8849
0.8869
0.8888
0.8907
0.8925
0.8944
0.8962
0.8980
0.9015
1%
0.9032
0.9099
0.9131
0.9147
1.3
0.9049
0.9066
0.9082
0.9115
0.9162
0.9177
0.9319
1.4
0.9192
0.9207
0.9222
0.9236
0.9251
0.9265
0.9279
0.9292
0.9306
0.9332
0.9345
0.9357
0.9370
0.9382
0.9394
0.9406
0.9418
0.9429
0.9441
1.5
2 33
133
0.9452
0.9463
0.9474
0.9484
0.9495
0.9505
0.9515
0.9525
0.9535
0.9545
1.6
0.9582
1.7
0.9554
0.9564
0.9573
0.9591
0.9599
0.9608
0.9616
0.9625
0.9633
0.9649
1.8
0.9641
0.9656
0.9664
0.9671
0.9678
0.9686
0.9693
0.9699
0.9706
0.9713
1.9
0.9719
0.9726
0.9732
0.9738
0.9744
0.9750
0.9756
0.9761
0.9767
0.9778
0.9788
0.9798
2.0
0.9772
0.9783
0.9793
0.9803
0.9808
0.9812
0.9817
2.1
0.9821
0.9826
0.9830
0.9834
0.9838
0.9842
0.9846
0.9850
0.9854
0.9857
0.9871
0.9901
0.9878
2.2
0.9861
0.9864
0.9868
0.9875
0.9881
0.9884
0.9887
0.9890
0.9896
0.9904
0.9913
0.9893
0.9898
0.9906
0.9909
0.9911
0.9916
2.3
0.9927
0.9929
0.9918
0.9920
0.9922
0.9925
0.9931
0.9932
0.9934
0.9936
2.4
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0.06 0.07 0.08 0.09 0.0 0.01 0.02 0.03 0.04 0.05 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.0 0.5596 0.5987 0.5398 0.5636 0.1 0.5438 0.5478 0.5517 0.5557 0.5675 0.5714 0.5753 0.2 0.5871 0.5948 0.5793 0.5832 0.5910 0.6026 0.6064 0.6103 0.6141 0.6331 0.6368 0.6443 0.3 0.6179 0.6217 0.6255 0.6293 0.6406 0.6480 0.6517 0.6554 0.6664 0.6736 0.4 0.6591 0.6628 0.6700 0.6772 0.6808 0.6844 0.6879 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.7257 0.7580 0.7357 0.7422 0.6 0.7291 0.7324 0.7389 0.7454 0.7486 0.7517 0.7549 0.7611 0.7852 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7 0.8023 0.7881 0.7910 0.7939 0.7967 0.7995 0.8051 0.8078 0.8106 0.8133 0.8 98% 0.8389 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8508 0.8554 0.8577 1.0 0.8413 0.8438 0.8461 0.8485 0.8531 0.8599 0.8621 0.8643 0.8686 0.8729 1.1 0.8665 0.8708 0.8749 0.8770 0.8790 0.8810 0.8830 1% 0.8997 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.9015 1% 0.9032 0.9099 0.9131 0.9147 1.3 0.9049 0.9066 0.9082 0.9115 0.9162 0.9177 0.9319 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.5 2 33 133 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.6 0.9582 1.7 0.9554 0.9564 0.9573 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 0.9649 1.8 0.9641 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 0.9713 1.9 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 0.9778 0.9788 0.9798 2.0 0.9772 0.9783 0.9793 0.9803 0.9808 0.9812 0.9817 2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 0.9871 0.9901 0.9878 2.2 0.9861 0.9864 0.9868 0.9875 0.9881 0.9884 0.9887 0.9890 0.9896 0.9904 0.9913 0.9893 0.9898 0.9906 0.9909 0.9911 0.9916 2.3 0.9927 0.9929 0.9918 0.9920 0.9922 0.9925 0.9931 0.9932 0.9934 0.9936 2.4

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