TABLE 1 CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL DISTRIBUTION (Continued) Cumulative Entries in the table give the area under the curve to the left of the z value. For example, for z= 1.25, the cumulative probability is .8944. probability .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 5080 5120 5517 .0 5000 .5040 .5160 .5199 .5239 .5279 .5319 .5359 5714 .6103 .1 .5398 .5438 .5478 .5557 .5596 .5636 .5675 .5753 .2 5793 .5832 .5871 .5910 .5948 .5987 .6026 .6064 .6141 .3 .6179 .6217 .6255 .6293 .6331 .6368 .6406 .6443 .6480 .6517 .4 .6554 .6591 .6628 .6664 .6700 .6736 .6772 .6808 .6844 .6879 .5 .6915 .6950 .6985 .7019 .7054 .7088 7123 .7157 .7190 .7224 .6 .7257 .7291 .7324 .7357 .7389 .7422 .7454 .7486 .7517 .7549 .7611 .7910 .7 .7580 .7642 .7673 .7704 .7734 .7764 .7794 .7823 .7852 .8 .7881 .7939 .7967 .7995 .8023 .8051 .8078 8106 .8133 .9 .8159 .8186 .8212 .8238 .8264 .8289 .8315 .8340 .8365 .8389 .8413 .8643 1.0 .8438 .8461 .8485 .8508 .8531 .8554 .8577 .8599 .8621 1.1 .8665 .8686 .8708 .8729 .8749 .8770 .8790 .8810 .8830 1.2 .8849 .8869 .8888 .8907 .8925 .8944 .8962 .8980 .8997 .9015 1.3 .9032 .9049 .9066 .9082 .9099 .9115 .9131 .9147 .9162 .9177 1.4 .9192 9207 .9222 .9236 .9251 .9265 .9279 .9292 .9306 .9319 1.5 .9332 .9345 .9357 .9370 .9382 .9394 .9406 .9418 .9429 .9441 1.6 .9452 .9463 .9474 .9484 .9495 .9505 .9515 .9525 .9535 .9545 .9582 .9664 .9633 .9706 1.7 .9554 .9564 .9573 .9591 .9599 .9608 .9616 .9625 1.8 .9641 .9649 .9656 .9671 .9678 .9686 .9693 .9699 1.9 .9713 .9719 .9726 .9732 .9738 .9744 .9750 .9756 .9761 .9767 2.0 .9772 .9778 .9783 .9788 .9793 .9798 .9803 .9808 .9812 .9817 2.1 .9821 .9826 .9830 .9834 .9838 .9842 .9846 .9850 .9854 .9857 .9884 .9911 .9890 .9916 2.2 .9861 .9864 .9868 .9871 .9875 .9878 .9881 .9887 2.3 .9893 .9896 .9898 .9901 .9904 .9906 .9909 .9913 2.4 .9918 .9920 .9922 .9925 .9927 .9929 .9931 .9932 .9934 .9936 2.5 .9938 .9940 .9941 .9943 .9945 .9946 .9948 .9949 .9951 .9952 .9961 .9971 2.6 .9953 .9965 .9955 .9956 .9967 .9957 .9959 .9960 .9962 .9963 .9964 .9972 .9979 2.7 .9966 .9968 .9969 .9970 .9973 .9974 .9977 .9983 2.8 .9974 .9975 .9976 .9977 .9978 .9979 .9980 .9981 2.9 .9981 .9982 .9982 .9984 .9984 .9985 .9985 .9986 .9986 3.0 .9987 .9987 .9987 .9988 .9988 .9989 .9989 .9989 .9990 .9990

TABLE 1 CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL DISTRIBUTION (Continued) Cumulative Entries in the table give the area under the curve to the left of the z value. For example, for z= 1.25, the cumulative probability is .8944. probability .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 5080 5120 5517 .0 5000 .5040 .5160 .5199 .5239 .5279 .5319 .5359 5714 .6103 .1 .5398 .5438 .5478 .5557 .5596 .5636 .5675 .5753 .2 5793 .5832 .5871 .5910 .5948 .5987 .6026 .6064 .6141 .3 .6179 .6217 .6255 .6293 .6331 .6368 .6406 .6443 .6480 .6517 .4 .6554 .6591 .6628 .6664 .6700 .6736 .6772 .6808 .6844 .6879 .5 .6915 .6950 .6985 .7019 .7054 .7088 7123 .7157 .7190 .7224 .6 .7257 .7291 .7324 .7357 .7389 .7422 .7454 .7486 .7517 .7549 .7611 .7910 .7 .7580 .7642 .7673 .7704 .7734 .7764 .7794 .7823 .7852 .8 .7881 .7939 .7967 .7995 .8023 .8051 .8078 8106 .8133 .9 .8159 .8186 .8212 .8238 .8264 .8289 .8315 .8340 .8365 .8389 .8413 .8643 1.0 .8438 .8461 .8485 .8508 .8531 .8554 .8577 .8599 .8621 1.1 .8665 .8686 .8708 .8729 .8749 .8770 .8790 .8810 .8830 1.2 .8849 .8869 .8888 .8907 .8925 .8944 .8962 .8980 .8997 .9015 1.3 .9032 .9049 .9066 .9082 .9099 .9115 .9131 .9147 .9162 .9177 1.4 .9192 9207 .9222 .9236 .9251 .9265 .9279 .9292 .9306 .9319 1.5 .9332 .9345 .9357 .9370 .9382 .9394 .9406 .9418 .9429 .9441 1.6 .9452 .9463 .9474 .9484 .9495 .9505 .9515 .9525 .9535 .9545 .9582 .9664 .9633 .9706 1.7 .9554 .9564 .9573 .9591 .9599 .9608 .9616 .9625 1.8 .9641 .9649 .9656 .9671 .9678 .9686 .9693 .9699 1.9 .9713 .9719 .9726 .9732 .9738 .9744 .9750 .9756 .9761 .9767 2.0 .9772 .9778 .9783 .9788 .9793 .9798 .9803 .9808 .9812 .9817 2.1 .9821 .9826 .9830 .9834 .9838 .9842 .9846 .9850 .9854 .9857 .9884 .9911 .9890 .9916 2.2 .9861 .9864 .9868 .9871 .9875 .9878 .9881 .9887 2.3 .9893 .9896 .9898 .9901 .9904 .9906 .9909 .9913 2.4 .9918 .9920 .9922 .9925 .9927 .9929 .9931 .9932 .9934 .9936 2.5 .9938 .9940 .9941 .9943 .9945 .9946 .9948 .9949 .9951 .9952 .9961 .9971 2.6 .9953 .9965 .9955 .9956 .9967 .9957 .9959 .9960 .9962 .9963 .9964 .9972 .9979 2.7 .9966 .9968 .9969 .9970 .9973 .9974 .9977 .9983 2.8 .9974 .9975 .9976 .9977 .9978 .9979 .9980 .9981 2.9 .9981 .9982 .9982 .9984 .9984 .9985 .9985 .9986 .9986 3.0 .9987 .9987 .9987 .9988 .9988 .9989 .9989 .9989 .9990 .9990

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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Question

A population has a mean of 300 and a standard deviation of 60. Suppose a sample of size 100 is selected x bar and mean is used to estimate . Use z-table.

What is the probability that the sample mean will be within +/- 5 of the population mean (to 4 decimals)? (Round z value in intermediate calculations to 2 decimal places.)
What is the probability that the sample mean will be within +/- 17 of the population mean (to 4 decimals)? (Round z value in intermediate calculations to 2 decimal places.)

TABLE 1 CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL
DISTRIBUTION (Continued)
Cumulative
Entries in the table
give the area under the
curve to the left of the
z value. For example, for
z= 1.25, the cumulative
probability is .8944.
probability
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
5080
5120
5517
.0
5000
.5040
.5160
.5199
.5239
.5279
.5319
.5359
5714
.6103
.1
.5398
.5438
.5478
.5557
.5596
.5636
.5675
.5753
.2
5793
.5832
.5871
.5910
.5948
.5987
.6026
.6064
.6141
.3
.6179
.6217
.6255
.6293
.6331
.6368
.6406
.6443
.6480
.6517
.4
.6554
.6591
.6628
.6664
.6700
.6736
.6772
.6808
.6844
.6879
.5
.6915
.6950
.6985
.7019
.7054
.7088
7123
.7157
.7190
.7224
.6
.7257
.7291
.7324
.7357
.7389
.7422
.7454
.7486
.7517
.7549
.7611
.7910
.7
.7580
.7642
.7673
.7704
.7734
.7764
.7794
.7823
.7852
.8
.7881
.7939
.7967
.7995
.8023
.8051
.8078
8106
.8133
.9
.8159
.8186
.8212
.8238
.8264
.8289
.8315
.8340
.8365
.8389
.8413
.8643
1.0
.8438
.8461
.8485
.8508
.8531
.8554
.8577
.8599
.8621
1.1
.8665
.8686
.8708
.8729
.8749
.8770
.8790
.8810
.8830
1.2
.8849
.8869
.8888
.8907
.8925
.8944
.8962
.8980
.8997
.9015
1.3
.9032
.9049
.9066
.9082
.9099
.9115
.9131
.9147
.9162
.9177
1.4
.9192
9207
.9222
.9236
.9251
.9265
.9279
.9292
.9306
.9319
1.5
.9332
.9345
.9357
.9370
.9382
.9394
.9406
.9418
.9429
.9441
1.6
.9452
.9463
.9474
.9484
.9495
.9505
.9515
.9525
.9535
.9545
.9582
.9664
.9633
.9706
1.7
.9554
.9564
.9573
.9591
.9599
.9608
.9616
.9625
1.8
.9641
.9649
.9656
.9671
.9678
.9686
.9693
.9699
1.9
.9713
.9719
.9726
.9732
.9738
.9744
.9750
.9756
.9761
.9767
2.0
.9772
.9778
.9783
.9788
.9793
.9798
.9803
.9808
.9812
.9817
2.1
.9821
.9826
.9830
.9834
.9838
.9842
.9846
.9850
.9854
.9857
.9884
.9911
.9890
.9916
2.2
.9861
.9864
.9868
.9871
.9875
.9878
.9881
.9887
2.3
.9893
.9896
.9898
.9901
.9904
.9906
.9909
.9913
2.4
.9918
.9920
.9922
.9925
.9927
.9929
.9931
.9932
.9934
.9936
2.5
.9938
.9940
.9941
.9943
.9945
.9946
.9948
.9949
.9951
.9952
.9961
.9971
2.6
.9953
.9965
.9955
.9956
.9967
.9957
.9959
.9960
.9962
.9963
.9964
.9972
.9979
2.7
.9966
.9968
.9969
.9970
.9973
.9974
.9977
.9983
2.8
.9974
.9975
.9976
.9977
.9978
.9979
.9980
.9981
2.9
.9981
.9982
.9982
.9984
.9984
.9985
.9985
.9986
.9986
3.0
.9987
.9987
.9987
.9988
.9988
.9989
.9989
.9989
.9990
.9990

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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