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
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 8E
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I need help with this. please be careful and precise with final answer
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 = ☐
k=|
(Round to two decimal places as needed.)
Transcribed Image Text:Areas under the Normal Curve
☐ =
Areas under the Normal Curve
z
0.0043
0.0041
2
.00
.01
.02
.03
.04
.00
.01
.02
.03
.04
-3.4 0.0003 0.0003 0.0003 0.0003 0.0003
-3.3 0.0005 0.0005 0.0005 0.0004 0.0004
-3.2 0.0007 0.0007 0.0006 0.0006 0.0006
-3.1 0.0010 0.0009 0.0009 0.0009 0.0008
-3.0 0.0013 0.0013 0.0013 0.0012 0.0012
-2.9 0.0019 0.0018 0.0018 0.0017 0.0016
-2.8 0.0026 0.0025 0.0024 0.0023 0.0023
-2.7 0.0035 0.0034 0.0033 0.0032 0.0031
-2.6 0.0047 0.0045 0.0044
-2.5 0.0062 0.0060 0.0059 0.0057 0.0055
-2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068
-2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089
-2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116
-2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150
-2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192
-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
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 0.1539 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 0.4404
0.4364 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
.06
.07
.08
.09
.05
.06
0.0003 0.0003
0.0004 0.0004
0.0006 0.0006 0.0005 0.0005
0.0008 0.0008 0.0008 0.0007
0.0011 0.0011 0.0011 0.0010
.07
.08
0.0003 0.0003
0.0004 0.0004
.09
2
0.0002 -3.4
0.0003 -3.3
0.0005 -3.2
0.0007 -3.1
0.0010 -3.0
0.0016 0.0015 0.0015 0.0014
0.0022 0.0021 0.0021 0.0020
0.0030 0.0029 0.0028 0.0027
0.0026 2.7
0.0040 0.0039 0.0038 0.0037 0.0036 -2.6
0.0054 0.0052 0.0051 0.0049
0.0048 -2.5
0.0066 0.0064 -2.4
0.0087 0.0084 -2.3
0.0113 0.0110 -2.2
0.0146
0.0143 -2.1
0.0188
0.0239
0.0301
0.0375
0.0014 -2.9
0.0019 -2.8
0.0183 -2.0
0.0233 -1.9
0.0294 -1.8
1.7
1.8
2.0
1
1
2.9
3.0
¡A
.05
2
3.2 0.9993 0.9993 0.9994
3.3 0.9995 0.9995 0.9995
3.4 0.9997 0.9997 0.9997
.00
.01
.02
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.0
0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.1
0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.2
0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.3
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
0.9 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
0.8962 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
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
1.9 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
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
0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 2.9
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
0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.2
0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.3
Z
0.8944
.03
.04
0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 3.4
.05
.06
.07
.09
.08
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