1a. Fish weights have a mean of 3 pounds and a standard deviation of 0.5 pound. What percentage of these fish should be heavier than 4 pounds?Selection Group: Is the correct choice = 30.85%; 2.28%; 2.00%; 97.73%; or 69.15%1b. Heights at the shoulder for adults of a breed of dog are normally distributed with a mean of 22 inches and standard deviation of 4 inches. What shoulder height is the boundary of the tallest 10% of adult dogs of this breed? (be as close as our chart allows)Group of answer choices: Is the correct answer = 31.32 in; 26.00 in; 25.60 in; 27.12 in; or 16.88 in Cumulative Standard Normal Distribution Tables0.010.020.030.04 0.050.060.070.090.080.4721 0.4681 0.46410.4325 0.42860.42470.3974 0.3936 0.38970.38590.3483-0.500.03670.0294Z0.00-0.00 0.5000 0.4960 0.4920 0.4880 0.48400.4801 0.4761-0.10 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364-0.200.4207 0.4168 0.4129 0.4090 0.4052 0.4013-0.30 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520-0.40 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.31210.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776-0.60 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451-0.70 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148-0.80 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867-0.90 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611-1.00 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.14010.1379-1.10 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170-1.20 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985-1.30 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823-1.40 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681-1.50 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559-1.60 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455-1.70 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375-1.80 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301-1.90 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239-2.00 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183-2.10 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143-2.20 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110-2.30 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084-2.40 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064-2.500.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048-2.60 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036-2.70 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026-2.80 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019-2.90 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014-3.00 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010-3.10 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007-3.20 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005-3.30 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003-3.40 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002-3.500.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002-3.600.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001-3.70 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001-3.80 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001*Note: z-values less than -3.89 produce a probability of zero.0.02330.0002 0.00020.0002 0.0002Department of Mathematics, Sinclair Community College, Dayton, OH TABLE 1 CUMULATIVE PROBABILITIES FOR THE STANDARD NORMALDISTRIBUTION (Continued)Z4789 BAA93 29539 87 388 3561.01.11.2.0.15000 5040 .5080 5120 51605398 5438 5478 .5517 55575793 5832 5871 5910 5948.3 .6179 .6217 .6255 .6293 .63314 .6554 .6591.2.6628 .6664 .67001.3.001.61.8.012.5 99382.6 .99532.7 .99652.8 .99742.9 .9981.023.0 99870.03ZCumulativeprobability.04.7157 .7190.6915 69507257 .7291.7088 .7123.7422 .74547486 7517.8.8621917793196985 .7019 .70547324 .7357 .73897 .7580 7611 .7642 .7673 .7704 .7734 .7764 .7794 .78237881 .7910 .7939 .7967 .7995 8023 .8051 .8078 .8106.8159 .8186 .8212 .8238 .8264 .8289 .8315 .8340 .83658413 .8438 .8461.8485.8508 .8531 .8554 .8577 .8599.8643 .8665 .8686 .8708 .8729 .8749 8770 .8790 .8810 .8830.8849 .8869 .8888 .8907 .8925 .8944 .8962 .8980 .8997 9015.9032 9049 .9066 9082 .9099 9115 .9131 9147 91621.4 .9192 .9207 .9222 .9236 .9251 .9265 .9279 .9292 93061.5 .9332 9345 9357 9370 9382 9394 .9406 9418 9429 94419452 .94639474 9484 9495 .9505 9515 .9525 .9535 .95451.7 .9554 .9564 .9573 9582 .9591 .9599 .9608 .9616 9625 9633.9641 .9649 .9656 9664 .9671 .9678 .9686 .9693 .9699 .97061.9 .9713 .9719 .9726 .9732 9738 .9744 9750 9756 9761 .97672.0 9772 9778 9783 9788 97932.1 9821 .9826 .9830 .9834 .98382.2 9861 9864 9868 9871 98752.3 9893 .9896 9898 9901 99042.4 9918 9920 9922 9925 9927.9940 9941 .9943 9945 .9946 9948.9955 9956 9957 9959 .9960 .9961.9966 9967 .9968 9969 .9970 9971 .9972 .9973.9975 .9976 .9977 9977 .9978 .9979 9979 9980.9982 .9982 .9983 .9984 .9984 9985 9985 .99869987 .9987 .9988.9949 9951.9962 9963.9988 99899989 9989.9990 .9990.05Entries in the tablegive the area under thecurve to the left of thez value. For example, forz = 1.25, the cumulativeprobability is .8944..06.07.08.5199 5239 .5279 5319.5596 5636 .5675 5714.5987 .6026 .6064 .6103.6368.6736.6406 .6443.6808.6772.095359.5753.6141.6480 6517.6844 .6879.7224.75497852.8133.83899817.9798 .9803 .9808 9812.9842 .9846 .9850 .9854 .98579878 .9881 .9884 9887 .9890.9906 .9909 .9911 9913 9916.9929 .9931 .9932 9934 9936995299649974.9981.9986

Answered: a. Fish weights have a mean of 3 pounds…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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100%

1a. Fish weights have a mean of 3 pounds and a standard deviation of 0.5 pound. What percentage of these fish should be heavier than 4 pounds?

Selection Group: Is the correct choice = 30.85%; 2.28%; 2.00%; 97.73%; or 69.15%

1b. Heights at the shoulder for adults of a breed of dog are normally distributed with a mean of 22 inches and standard deviation of 4 inches. What shoulder height is the boundary of the tallest 10% of adult dogs of this breed? (be as close as our chart allows)

Group of answer choices: Is the correct answer = 31.32 in; 26.00 in; 25.60 in; 27.12 in; or 16.88 in

Cumulative Standard Normal Distribution Table
s
0.01
0.02
0.03
0.04 0.05
0.06
0.07
0.09
0.08
0.4721 0.4681 0.4641
0.4325 0.4286
0.4247
0.3974 0.3936 0.3897
0.3859
0.3483
-0.50
0.0367
0.0294
Z
0.00
-0.00 0.5000 0.4960 0.4920 0.4880 0.4840
0.4801 0.4761
-0.10 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364
-0.20
0.4207 0.4168 0.4129 0.4090 0.4052 0.4013
-0.30 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520
-0.40 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121
0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776
-0.60 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451
-0.70 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148
-0.80 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867
-0.90 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611
-1.00 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401
0.1379
-1.10 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170
-1.20 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985
-1.30 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823
-1.40 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681
-1.50 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559
-1.60 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455
-1.70 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375
-1.80 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301
-1.90 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239
-2.00 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183
-2.10 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143
-2.20 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110
-2.30 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084
-2.40 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064
-2.50
0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048
-2.60 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036
-2.70 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026
-2.80 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019
-2.90 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014
-3.00 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010
-3.10 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007
-3.20 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005
-3.30 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003
-3.40 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002
-3.50
0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
-3.60
0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
-3.70 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
-3.80 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
*Note: z-values less than -3.89 produce a probability of zero.
0.0233
0.0002 0.0002
0.0002 0.0002
Department of Mathematics, Sinclair Community College, Dayton, OH

TABLE 1 CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL
DISTRIBUTION (Continued)
Z
4789 BAA93 29539 87 388 3
5
6
1.0
1.1
1.2
.0
.1
5000 5040 .5080 5120 5160
5398 5438 5478 .5517 5557
5793 5832 5871 5910 5948
.3 .6179 .6217 .6255 .6293 .6331
4 .6554 .6591
.2
.6628 .6664 .6700
1.3
.00
1.6
1.8
.01
2.5 9938
2.6 .9953
2.7 .9965
2.8 .9974
2.9 .9981
.02
3.0 9987
0
.03
Z
Cumulative
probability
.04
.7157 .7190
.6915 6950
7257 .7291
.7088 .7123
.7422 .7454
7486 7517
.8
.8621
9177
9319
6985 .7019 .7054
7324 .7357 .7389
7 .7580 7611 .7642 .7673 .7704 .7734 .7764 .7794 .7823
7881 .7910 .7939 .7967 .7995 8023 .8051 .8078 .8106
.8159 .8186 .8212 .8238 .8264 .8289 .8315 .8340 .8365
8413 .8438 .8461
.8485
.8508 .8531 .8554 .8577 .8599
.8643 .8665 .8686 .8708 .8729 .8749 8770 .8790 .8810 .8830
.8849 .8869 .8888 .8907 .8925 .8944 .8962 .8980 .8997 9015
.9032 9049 .9066 9082 .9099 9115 .9131 9147 9162
1.4 .9192 .9207 .9222 .9236 .9251 .9265 .9279 .9292 9306
1.5 .9332 9345 9357 9370 9382 9394 .9406 9418 9429 9441
9452 .9463
9474 9484 9495 .9505 9515 .9525 .9535 .9545
1.7 .9554 .9564 .9573 9582 .9591 .9599 .9608 .9616 9625 9633
.9641 .9649 .9656 9664 .9671 .9678 .9686 .9693 .9699 .9706
1.9 .9713 .9719 .9726 .9732 9738 .9744 9750 9756 9761 .9767
2.0 9772 9778 9783 9788 9793
2.1 9821 .9826 .9830 .9834 .9838
2.2 9861 9864 9868 9871 9875
2.3 9893 .9896 9898 9901 9904
2.4 9918 9920 9922 9925 9927
.9940 9941 .9943 9945 .9946 9948
.9955 9956 9957 9959 .9960 .9961
.9966 9967 .9968 9969 .9970 9971 .9972 .9973
.9975 .9976 .9977 9977 .9978 .9979 9979 9980
.9982 .9982 .9983 .9984 .9984 9985 9985 .9986
9987 .9987 .9988
.9949 9951
.9962 9963
.9988 9989
9989 9989
.9990 .9990
.05
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.
.06
.07
.08
.5199 5239 .5279 5319
.5596 5636 .5675 5714
.5987 .6026 .6064 .6103
.6368
.6736
.6406 .6443
.6808
.6772
.09
5359
.5753
.6141
.6480 6517
.6844 .6879
.7224
.7549
7852
.8133
.8389
9817
.9798 .9803 .9808 9812
.9842 .9846 .9850 .9854 .9857
9878 .9881 .9884 9887 .9890
.9906 .9909 .9911 9913 9916
.9929 .9931 .9932 9934 9936
9952
9964
9974
.9981
.9986

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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