The weights of a large number of miniature poodles are approximately normally distributed with a mean of 8 kilograms and a standard deviation of 0.9 kilogram. If measurements are recorded to the nearest tenth of a kilogram, find the proportion of these poodles with weights (a) over 9.5 kilograms; (b) of at most 8.5 kilograms; (c) between 7.5 and 9.2 kilograms inclusive. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) The proportion of these poodles with weights over 9.5 kilograms is (Round to four decimal places as needed.) (b) The proportion of these poodles with weights of at most 8.5 kilograms is (Round to four decimal places as needed.) (c) The proportion of these poodles with weights between 7.5 and 9.2 kilograms inclusive is ☐ (Round to four decimal places as needed.)
The weights of a large number of miniature poodles are approximately normally distributed with a mean of 8 kilograms and a standard deviation of 0.9 kilogram. If measurements are recorded to the nearest tenth of a kilogram, find the proportion of these poodles with weights (a) over 9.5 kilograms; (b) of at most 8.5 kilograms; (c) between 7.5 and 9.2 kilograms inclusive. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) The proportion of these poodles with weights over 9.5 kilograms is (Round to four decimal places as needed.) (b) The proportion of these poodles with weights of at most 8.5 kilograms is (Round to four decimal places as needed.) (c) The proportion of these poodles with weights between 7.5 and 9.2 kilograms inclusive is ☐ (Round to four decimal places as needed.)
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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Transcribed Image Text:Areas under the Normal Curve
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Areas under the Normal Curve
0.0033
0.0044
0.1539
2
.00
.01
Z
.00
.01
.02
.03
.04
.05
.06
-3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003
-3.3
0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004
-3.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006
-3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008
-3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011
-2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015
-2.8
0.0026 0.0025 0.0024 0.0023 0.0023
0.0022
-2.7 0.0035 0.0034
0.0032 0.0031 0.0030
0.0027 0.0026 -2.7
-2.6 0.0047 0.0045
0.0043 0.0041 0.0040
0.0037 0.0036 -2.6
-2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054
0.0049 0.0048 -2.5
-2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 -2.4
-2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 -2.3
-2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 -2.2
-2.1
0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 -2.1
-2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 -2.0
-1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 -1.9
-1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 -1.8
-1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 -1.7
-1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 -1.6
-1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 -1.5
-1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 -1.4
-1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 -1.3
-1.2
0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985 -1.2
-1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190
0.1170 -1.1
-1.0
0.1587 0.1562
0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 -1.0
-0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635
-0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.8
-0.7
0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 -0.7
-0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 -0.6
-0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843
0.2810
0.2776 -0.5
-0.4 0.3446 0.3409 0.3372 0.3336
0.3300
0.3264 0.3228 0.3192 0.3156
0.3121 -0.4
-0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483 -0.3
-0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 -0.2
-0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325
0.4247 -0.1
-0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721
0.4641 -0.0
.02
.03
.04
.05
.06
.07
.09
.07
.08
.09
%
0.0003 0.0003 0.0002 -3.4
0.0004 0.0004 0.0003 -3.3
0.0005 0.0005 0.0005
-3.2
0.0008 0.0007 0.0007 -3.1
0.0011 0.0010 0.0010 -3.0
0.0015 0.0014 0.0014 -2.9
2
0.0021 0.0021 0.0020 0.0019 -2.8
0.0029 0.0028
0.0039 0.0038
0.0052 0.0051
0.9
0.1611 -0.9
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0.4286
0.4681
.08
1:1
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A
.00
.01
.02
.03
0.0 0.5000 0.5040 0.5080
0.5120
0.1 0.5398 0.5438 0.5478 0.5517
0.2 0.5793 0.5832 0.5871 0.5910 0.5948
0.3 0.6179 0.6217 0.6255 0.6293 0.6331
0.4 0.6554 0.6591 0.6628 0.6664 0.6700
0.6736 0.6772 0.6808 0.6844 0.6879 0.4
0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.5
0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.6
0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734
0.7764 0.7794 0.7823 0.7852 0.7
0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.8
0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 0.9
1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531
0.8554 0.8577 0.8599 0.8621 1.0
1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 1.1
1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.2
1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.3
1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.4
1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.5
1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.6
1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.7
1.8 0.9641
0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.8
1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 1.9
2.0 0.9772 0.9778 0,9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.0
2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0,9850 0.9854 0.9857 2.1
2.2 0.9861 0.9864 0.9868 0.9871
0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 2.2
2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0,9906 0,9909 0.9911
0.9913 0.9916 2.3
2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.4
2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.5
2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.6
2.7
0.9965 0.9966 0.9967 0.9968 0.9969
0.9970 0.9971 0.9972 0.9973 0.9974 2.7
2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.8
2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 2.9
3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.0
3.1
0.9992 0.9993 0.9993 3.1
3.2
3.3
.04
.05
.06
.07
.08
.09
0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.0
0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.1
0.5987 0.6026 0.6064 0.6103 0.6141 0.2
0.6368 0.6406 0.6443 0.6480 0.6517 0.3
2
3.4
2
.00
.01
0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992
0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.2
0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.3
0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 3.4
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.03
.04
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Transcribed Image Text:The weights of a large number of miniature poodles are approximately normally distributed with a mean of 8
kilograms and a standard deviation of 0.9 kilogram. If measurements are recorded to the nearest tenth of a kilogram,
find the proportion of these poodles with weights
(a) over 9.5 kilograms;
(b) of at most 8.5 kilograms;
(c) between 7.5 and 9.2 kilograms inclusive.
Click here to view page 1 of the standard normal distribution table.
Click here to view page 2 of the standard normal distribution table.
(a) The proportion of these poodles with weights over 9.5 kilograms is
(Round to four decimal places as needed.)
(b) The proportion of these poodles with weights of at most 8.5 kilograms is
(Round to four decimal places as needed.)
(c) The proportion of these poodles with weights between 7.5 and 9.2 kilograms inclusive is
(Round to four decimal places as needed.)
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