An admissions director wants to estimate the mean age of all students enrolled at a college. The estimate must be within 1.4 years of the population mean. Assume the population of ages is normally distributed. (a) Determine the minimum sample size required to construct a 90% confidence interval for the population mean. Assume the population standard deviation is 1.8 years. (b) The sample mean is 20 years of age. Using the minimum sample size with a 90% level of confidence, does it seem likely that the population mean could be within 9% of the sample mean? within 10% of the sample mean? Explain. Click here to view page 1 of the Standard Normal Table. LOADING... Click here to view page 2 of the Standard Normal Table. LOADING... The 90% confidence interval is (enter your response here , enter your response here ). It ▼ likely that the population mean could be within 9% of the sample mean because the interval formed by the values 9% away from the sample mean ▼ the confidence interval. It ▼ likely that the population mean could be within 10% of the sample mean because the interval formed by the values 10% away from the sample mean ▼ the confidence interval. (Round to two decimal places as needed.) z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 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 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 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 2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
An admissions director wants to estimate the mean age of all students enrolled at a college. The estimate must be within 1.4 years of the population mean. Assume the population of ages is normally distributed. (a) Determine the minimum sample size required to construct a 90% confidence interval for the population mean. Assume the population standard deviation is 1.8 years. (b) The sample mean is 20 years of age. Using the minimum sample size with a 90% level of confidence, does it seem likely that the population mean could be within 9% of the sample mean? within 10% of the sample mean? Explain. Click here to view page 1 of the Standard Normal Table. LOADING... Click here to view page 2 of the Standard Normal Table. LOADING... The 90% confidence interval is (enter your response here , enter your response here ). It ▼ likely that the population mean could be within 9% of the sample mean because the interval formed by the values 9% away from the sample mean ▼ the confidence interval. It ▼ likely that the population mean could be within 10% of the sample mean because the interval formed by the values 10% away from the sample mean ▼ the confidence interval. (Round to two decimal places as needed.) z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 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 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 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 2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
An admissions director wants to estimate the mean age of all students enrolled at a college. The estimate must be within
1.4
years of the population mean. Assume the population of ages is normally distributed.(a) Determine the minimum sample size required to construct a
90%
confidence interval for the population mean. Assume the population standard deviation is
1.8
years.(b) The sample mean is
20
years of age. Using the minimum sample size with a
90%
level of confidence, does it seem likely that the population mean could be within
9%
of the sample mean? within
10%
of the sample mean? Explain.Click here to view page 1 of the Standard Normal Table.
Click here to view page 2 of the Standard Normal Table.
LOADING...
LOADING...
The
likely that the population mean could be within
the confidence interval. It
likely that the population mean could be within
the confidence interval.
90%
confidence interval is
(enter your response here
,
enter your response here
).
It
▼
9%
of the sample mean because the interval formed by the values
9%
away from the sample mean
▼
▼
10%
of the sample mean because the interval formed by the values
10%
away from the sample mean
▼
(Round to two decimal places as needed.)
|
z
|
0.00
|
0.01
|
0.02
|
0.03
|
0.04
|
0.05
|
0.06
|
0.07
|
0.08
|
0.09
|
|---|---|---|---|---|---|---|---|---|---|---|
|
0.0
|
0.5000
|
0.5040
|
0.5080
|
0.5120
|
0.5160
|
0.5199
|
0.5239
|
0.5279
|
0.5319
|
0.5359
|
|
0.1
|
0.5398
|
0.5438
|
0.5478
|
0.5517
|
0.5557
|
0.5596
|
0.5636
|
0.5675
|
0.5714
|
0.5753
|
|
0.2
|
0.5793
|
0.5832
|
0.5871
|
0.5910
|
0.5948
|
0.5987
|
0.6026
|
0.6064
|
0.6103
|
0.6141
|
|
0.3
|
0.6179
|
0.6217
|
0.6255
|
0.6293
|
0.6331
|
0.6368
|
0.6406
|
0.6443
|
0.6480
|
0.6517
|
|
0.4
|
0.6554
|
0.6591
|
0.6628
|
0.6664
|
0.6700
|
0.6736
|
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
|
|
0.6
|
0.7257
|
0.7291
|
0.7324
|
0.7357
|
0.7389
|
0.7422
|
0.7454
|
0.7486
|
0.7517
|
0.7549
|
|
0.7
|
0.7580
|
0.7611
|
0.7642
|
0.7673
|
0.7704
|
0.7734
|
0.7764
|
0.7794
|
0.7823
|
0.7852
|
|
0.8
|
0.7881
|
0.7910
|
0.7939
|
0.7967
|
0.7995
|
0.8023
|
0.8051
|
0.8078
|
0.8106
|
0.8133
|
|
0.9
|
0.8159
|
0.8186
|
0.8212
|
0.8238
|
0.8264
|
0.8289
|
0.8315
|
0.8340
|
0.8365
|
0.8389
|
|
1.0
|
0.8413
|
0.8438
|
0.8461
|
0.8485
|
0.8508
|
0.8531
|
0.8554
|
0.8577
|
0.8599
|
0.8621
|
|
1.1
|
0.8643
|
0.8665
|
0.8686
|
0.8708
|
0.8729
|
0.8749
|
0.8770
|
0.8790
|
0.8810
|
0.8830
|
|
1.2
|
0.8849
|
0.8869
|
0.8888
|
0.8907
|
0.8925
|
0.8944
|
0.8962
|
0.8980
|
0.8997
|
0.9015
|
|
1.3
|
0.9032
|
0.9049
|
0.9066
|
0.9082
|
0.9099
|
0.9115
|
0.9131
|
0.9147
|
0.9162
|
0.9177
|
|
1.4
|
0.9192
|
0.9207
|
0.9222
|
0.9236
|
0.9251
|
0.9265
|
0.9279
|
0.9292
|
0.9306
|
0.9319
|
|
1.5
|
0.9332
|
0.9345
|
0.9357
|
0.9370
|
0.9382
|
0.9394
|
0.9406
|
0.9418
|
0.9429
|
0.9441
|
|
1.6
|
0.9452
|
0.9463
|
0.9474
|
0.9484
|
0.9495
|
0.9505
|
0.9515
|
0.9525
|
0.9535
|
0.9545
|
|
1.7
|
0.9554
|
0.9564
|
0.9573
|
0.9582
|
0.9591
|
0.9599
|
0.9608
|
0.9616
|
0.9625
|
0.9633
|
|
1.8
|
0.9641
|
0.9649
|
0.9656
|
0.9664
|
0.9671
|
0.9678
|
0.9686
|
0.9693
|
0.9699
|
0.9706
|
|
1.9
|
0.9713
|
0.9719
|
0.9726
|
0.9732
|
0.9738
|
0.9744
|
0.9750
|
0.9756
|
0.9761
|
0.9767
|
|
2.0
|
0.9772
|
0.9778
|
0.9783
|
0.9788
|
0.9793
|
0.9798
|
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
|
|
2.2
|
0.9861
|
0.9864
|
0.9868
|
0.9871
|
0.9875
|
0.9878
|
0.9881
|
0.9884
|
0.9887
|
0.9890
|
|
2.3
|
0.9893
|
0.9896
|
0.9898
|
0.9901
|
0.9904
|
0.9906
|
0.9909
|
0.9911
|
0.9913
|
0.9916
|
|
2.4
|
0.9918
|
0.9920
|
0.9922
|
0.9925
|
0.9927
|
0.9929
|
0.9931
|
0.9932
|
0.9934
|
0.9936
|
|
2.5
|
0.9938
|
0.9940
|
0.9941
|
0.9943
|
0.9945
|
0.9946
|
0.9948
|
0.9949
|
0.9951
|
0.9952
|
|
2.6
|
0.9953
|
0.9955
|
0.9956
|
0.9957
|
0.9959
|
0.9960
|
0.9961
|
0.9962
|
0.9963
|
0.9964
|
|
2.7
|
0.9965
|
0.9966
|
0.9967
|
0.9968
|
0.9969
|
0.9970
|
0.9971
|
0.9972
|
0.9973
|
0.9974
|
|
2.8
|
0.9974
|
0.9975
|
0.9976
|
0.9977
|
0.9977
|
0.9978
|
0.9979
|
0.9979
|
0.9980
|
0.9981
|
|
2.9
|
0.9981
|
0.9982
|
0.9982
|
0.9983
|
0.9984
|
0.9984
|
0.9985
|
0.9985
|
0.9986
|
0.9986
|
|
3.0
|
0.9987
|
0.9987
|
0.9987
|
0.9988
|
0.9988
|
0.9989
|
0.9989
|
0.9989
|
0.9990
|
0.9990
|
|
3.1
|
0.9990
|
0.9991
|
0.9991
|
0.9991
|
0.9992
|
0.9992
|
0.9992
|
0.9992
|
0.9993
|
0.9993
|
|
3.2
|
0.9993
|
0.9993
|
0.9994
|
0.9994
|
0.9994
|
0.9994
|
0.9994
|
0.9995
|
0.9995
|
0.9995
|
|
3.3
|
0.9995
|
0.9995
|
0.9995
|
0.9996
|
0.9996
|
0.9996
|
0.9996
|
0.9996
|
0.9996
|
0.9997
|
|
3.4
|
0.9997
|
0.9997
|
0.9997
|
0.9997
|
0.9997
|
0.9997
|
0.9997
|
0.9997
|
0.9997
|
0.9998
|
|
z
|
0.00
|
0.01
|
0.02
|
0.03
|
0.04
|
0.05
|
0.06
|
0.07
|
0.08
|
0.09
|
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Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman