Suppose we use the mean of a random sample of size n = 100 to estimate the mean of a population with σ = 30 . Use the central limit theorem to compute the probability that the error is less than 6. Express your answer as a decimal using 4 decimal places. Give the exact value on the chart. Do not round your answer.....

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 31PPS
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Suppose we use the mean of a random sample of size n = 100 to estimate the mean of a population with σ = 30 . Use the central limit theorem to compute the probability that the error is less than 6. Express your answer as a decimal using 4 decimal places. Give the exact value on the chart. Do not round your answer.....
TABLE II Normal-Curve Areas
Z
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
0.0
.0000
.0040
.0080
0.1
.0398
.0438
.0478
0.2
.0793
.0832
0.3
.1179
.1217
0.4
.1554
.1591
0.5
.1915
.1950
.0120 .0160
.0517 .0557
.0871 .0910. .0948
.1255 .1293 .1331
.1628 .1664 .1700
.1985 .2019 .2054
.0199 .0239 .0279 .0319 .0359
.0596 .0636 .0675 .0714 .0753
.0987 .1026 .1064 .1103 .1141
.1368 .1406 .1443 .1480 .1517
.1736 .1772 .1808 .1844 .1879
.2088 .2123 .2157 .2190 .2224
0.6
.2257
.2291
.2324
.2357
0.7
2580
.2611
.2642
.2673
.2389 .2422
.2704 .2734
0.8
.2881
.2910
.2939
.2967
.2995
.3023
0.9
.3159 .3186 .3212
.3238
.3264
.3289
1.0
.3413
.3438
.3461
.3485
.3508
.3531
.2454 .2486 .2517 .2549
.2764 .2794 .2823 .2852
.3051 .3078 .3106 .3133
.3315 .3340 .3365 .3389
.3554 .3577 .3599 .3621
1.1
.3643
.3665
.3686
.3708
.3729
.3749
.3770 .3790
.3810 .3830
1.2
.3849
.3869
.3888
.3907
.3925
1.3
.4032
.4049
.4066
.4082
.3944 .3962 .3980
.4099 .4115 .4131
.3997 .4015
1.4
.4192 .4207
.4222
.4236
.4147 .4162 .4177
.4251. .4265 .4279 .4292 .4306
.4319
1.5
.4332
.4345
.4357
.4370
.4382 .4394 .4406 .4418 .4429
.4441
1.6
.4452 .4463
.4474
.4484
1.7
.4554 .4564
.4573 .4582
.4495 .4505
.4591 .4599
1.8
.4641 .4649
.4656
.4664
1.9
.4713 .4719 .4726
2.0
.4772
.4732
.4778 .4783 .4788
.4515 .4525 .4535
.4608 .4616 .4625 .4633
.4671 .4678 .4686 .4693 .4699 .4706
.4738 .4744 .4750 .4756
.4793 .4798 .4803 .4808
.4545
.4761 .4767
.4812 .4817
2.4
2.5
22222
2.1
.4821 .4826 .4830 .4834 .4838 .4842
.4861 .4864 .4868 .4871
.4878
.4875
2.3
.4893
.4896 .4898
.4901
.4904
.4906
.4846 .4850 .4854 .4857
.4881 .4884 .4887 .4890
.4909
.4911 .4913
.4916
.4918 .4920 .4922
.4925
.4927
.4929
.4931
.4938
.4940
.4941
.4943 .4945
.4946 .4948
.4932 .4934
.4949
.4936
.4951 .4952
2.6
.4953 .4955
.4956
.4957
.4959
.4960
.4961
2.7
.4965 .4966
.4967
.4968
.4969
.4970
.4971
2.8
.4974
.4975 .4976 .4977
.4977
.4978
.4962 .4963 .4964
.4972 .4973 .4974
.4979 .4979 .4980 .4981
2.9
.4981 4982 .4982
.4983
.4984
.4984
.4985
.4985
.4986 .4986
3.0
.4987
.4987
4987
.4988
.4988
.4989
.4989 .4989
.4990
.4990
Also, for z=4.0, 5.0, and 6.0, the areas are 0.49997, 0.4999997, and 0.499999999.
Transcribed Image Text:TABLE II Normal-Curve Areas Z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 0.0 .0000 .0040 .0080 0.1 .0398 .0438 .0478 0.2 .0793 .0832 0.3 .1179 .1217 0.4 .1554 .1591 0.5 .1915 .1950 .0120 .0160 .0517 .0557 .0871 .0910. .0948 .1255 .1293 .1331 .1628 .1664 .1700 .1985 .2019 .2054 .0199 .0239 .0279 .0319 .0359 .0596 .0636 .0675 .0714 .0753 .0987 .1026 .1064 .1103 .1141 .1368 .1406 .1443 .1480 .1517 .1736 .1772 .1808 .1844 .1879 .2088 .2123 .2157 .2190 .2224 0.6 .2257 .2291 .2324 .2357 0.7 2580 .2611 .2642 .2673 .2389 .2422 .2704 .2734 0.8 .2881 .2910 .2939 .2967 .2995 .3023 0.9 .3159 .3186 .3212 .3238 .3264 .3289 1.0 .3413 .3438 .3461 .3485 .3508 .3531 .2454 .2486 .2517 .2549 .2764 .2794 .2823 .2852 .3051 .3078 .3106 .3133 .3315 .3340 .3365 .3389 .3554 .3577 .3599 .3621 1.1 .3643 .3665 .3686 .3708 .3729 .3749 .3770 .3790 .3810 .3830 1.2 .3849 .3869 .3888 .3907 .3925 1.3 .4032 .4049 .4066 .4082 .3944 .3962 .3980 .4099 .4115 .4131 .3997 .4015 1.4 .4192 .4207 .4222 .4236 .4147 .4162 .4177 .4251. .4265 .4279 .4292 .4306 .4319 1.5 .4332 .4345 .4357 .4370 .4382 .4394 .4406 .4418 .4429 .4441 1.6 .4452 .4463 .4474 .4484 1.7 .4554 .4564 .4573 .4582 .4495 .4505 .4591 .4599 1.8 .4641 .4649 .4656 .4664 1.9 .4713 .4719 .4726 2.0 .4772 .4732 .4778 .4783 .4788 .4515 .4525 .4535 .4608 .4616 .4625 .4633 .4671 .4678 .4686 .4693 .4699 .4706 .4738 .4744 .4750 .4756 .4793 .4798 .4803 .4808 .4545 .4761 .4767 .4812 .4817 2.4 2.5 22222 2.1 .4821 .4826 .4830 .4834 .4838 .4842 .4861 .4864 .4868 .4871 .4878 .4875 2.3 .4893 .4896 .4898 .4901 .4904 .4906 .4846 .4850 .4854 .4857 .4881 .4884 .4887 .4890 .4909 .4911 .4913 .4916 .4918 .4920 .4922 .4925 .4927 .4929 .4931 .4938 .4940 .4941 .4943 .4945 .4946 .4948 .4932 .4934 .4949 .4936 .4951 .4952 2.6 .4953 .4955 .4956 .4957 .4959 .4960 .4961 2.7 .4965 .4966 .4967 .4968 .4969 .4970 .4971 2.8 .4974 .4975 .4976 .4977 .4977 .4978 .4962 .4963 .4964 .4972 .4973 .4974 .4979 .4979 .4980 .4981 2.9 .4981 4982 .4982 .4983 .4984 .4984 .4985 .4985 .4986 .4986 3.0 .4987 .4987 4987 .4988 .4988 .4989 .4989 .4989 .4990 .4990 Also, for z=4.0, 5.0, and 6.0, the areas are 0.49997, 0.4999997, and 0.499999999.
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