Given a standard normal distribution, find the value of k such that (a) P(Z > k) = 0.2578; (b) P(Z
Given a standard normal distribution, find the value of k such that (a) P(Z > k) = 0.2578; (b) P(Z
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
z
.09
.00
.01
.02
.03
.04
.05
.06
.07
.08
-3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 -3.4
-3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004
0.0004 0.0004 0.0004 0.0003 -3.3
-3.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005
0.0005 0.0005 -3.2
-3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 -3.1
-3.0 0.0013 0.0013 0.0013 0.0012 0.0012
0.0011 0.0011 0.0011 0.0010 0.0010 -3.0
☑=
Areas under the Normal Curve
z
0.0
+
2.
2.
2
.00
.01
.02
.03
.04
-2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016
0.0014 0.0014 -2.9
-2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 -2.8
-2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027
-2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038
0.0037
-2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049
-2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066
-2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087
-2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113
-2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154
0.0150 0.0146
-2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188
-1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244
-1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307
-1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384
-1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475
-1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582
-1.4 0.0808 0.0793 0.0778 0.0764 0.0749
0.0735 0.0721 0.0708
-1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853
-1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020
-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 0.1539 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 0.1611 -0.9
-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
0.4325 0.4286 0.4247 -0.1
-0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641 -0.0
.05
.07
.08
.09
0.0015 0.0015
0.0026 -2.7
0.0036 -2.6
0.0048 -2.5
.00
.01
.02
.03
.04
.05
0.5000 0.5040 0.5080 0.5120 0.5160 0.5199
0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596
0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987
0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368
0.4 0,6554 0.6591 0.6628 0.6664 0.6700 0.6736
0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.5
0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.6
0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.7
.06
.07
.08
.09
0.5239 0.5279 0.5319 0.5359 0.0
0.5636 0.5675 0.5714 0.5753 0.1
0.6026 0.6064 0.6103 0.6141 0.2
0.6406 0.6443 0.6480 0.6517 0.3
0.6772 0.6808 0.6844 0.6879 0.4
0.0064 -2.4
1.0
0.0084 -2.3
0.0110 -2.2
0.0143 -2.1
0.0183 -2.0
0.0239
0.0301 0.0294 -1.8
0.0375 0.0367 -1.7
0.0465 0.0455 -1.6
0.0571 0.0559 -1.5
0.0694 0.0681 -1.4
0.0838 0.0823 -1.3
0.1003 0.0985 -1.2
0.0233 -1.9
1.8
1.9
2.0
2.1
2.2
0.4404
0.4364
¡Ai
.06
2
.00
.01
.02
0.5
0.6 0.7257
0.7 0.7580
0.8 0.7881 0.7910 0.7939 0.7967 0.7995
0.8051
0.8078 0.8106 0.8133 0.8
0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 0.9
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
0.9641 0.9649 0.9656 0.9664 0.9671 0.9678
0.9686 0.9693 0.9699 0.9706 1.8
0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 1.9
0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.0
0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.1
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 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 3.1
3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.2
3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.3
3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997
0.9997 0.9997 0.9998 3.4
.03
.04
.05
.06
.07
.08
.09
0.8023
z
Transcribed Image Text:Given a standard normal distribution, find the value of k such that
(a) P(Z>k) 0.2578;
(b) P(Z<k) 0.0401;
(c) P(-0.95<Z<k) = 0.7269.
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) k = ☐
(Round to two decimal places as needed.)
(b) k = ☐
(Round to two decimal places as needed.)
(c) k = ☐
(Round to two decimal places as needed.)
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