1-What is the probability that an observation on the standard normal distributio
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Question
1-What is the probability that an observation on the standard normal distribution falls above z-score 1.96.
2-What is the probability that an observation on the standard normal distribution falls above z-score -1.96.
3-What is the probability that an observation on the standard normal distribution falls between z-score 0.65 and z-score 2.65.
4-Find z-score A that satisfies the following statement. The probability that an observation on the standard normal distribution falls below z-score A is 0.9951.
Standard Normal Distribution Table (Right-Tail Probabilities) 01 02 03 04 05 06 07 08 09 0.0 5000 4960 4920 4880 4840 4801 4761 4721 4681 4641 0.1 4602 4562 4522 4483 4443 4404 4364 4325 4286 4247 0.24207 4168 4129 4090 4052 4013 .3974 .3936 .3897 3859 0.33821 3783 .3745.3707 .3669 3632 .3594 3557 .3520 3483 0.4 3446 3409 .3372.3336 .3300 3264 .3228 .3192 3156 3121 0.5 3085 3050 .3015 .2981 .2946 2912 .2877 2843 2810 2776 0.6 2743 2709 .2676.2643 .2611 2578 2546 2514 2483 2451 0.7 2420 2389 2358.2327 .2296 2266 2236 2206 2177 2148 0.81.2119 .2090 .2061 .2033 .2005 .1977 .1949 .1922 .1894 .1867 0.91.1841 .1814 .1788 .1762 .1736 .1711 .1685 .1660 .1635 .1611 1.01.1587 .1562 .1539 .1515 .1492 .1469 .1446 .1423 .1401 .1379 1.11.1357 .1335 .1314 .1292 .1271 .1251 .1230 .1210 .1190 .1170 1.21.1151 .1131 .1112 .1093 .1075 .1056 .1038 .1020 .1003 .0985 1.3 0968 0951 .0934 .0918 0901 0885 .0869 0853 0838 0823 1.40808 0793 0778 0764 0749 0735 0721 0708 0694 0681 1.5 0668 0655 0643 0630 0618 0606 .0594 0582 0571 0559 1.6 0548 0537 .0526 0516 0505 0495 0485 0475 0465 0455 1.7 0446 0436 0427 0418 0409 0401 .0392 0384 0375 0367 1.8 0359 0351 0344 0336 0329 0322 .0314 0307 0301 0294 1.90287 0281 0274 0268 0262 0256 0250 0244 0239 0233 2.00228 0222 0217 .0212 .0207 0202 .0197 0192 0188 0183 2.10179 0174 0170.0166 0162 .0158 .0154 0150 0146 0143 2.20139 0136 0132 .0129 .0125 .0122 .0119 0116 0113 0110 2.30107 0104 .0102 .0099 0096 .0094 .0091 .0089 0087 0084 2.40082 0080 0078.0075 0073 .0071 0069 0068 0066 0064 2.5 0062 0060 0059 .0057 .0055 .0054 .0052 0051 0049 0048 2.6 0047 0045 .0044 .0043 0041 .0040 .0039 0038 0037 0036 2.70035 0034 .0033 .0032 0031 .0030 0029 0028 0027 .0026 2.8.0026 0025 .0024 .0023 0023 .0022 .0021 0021 0020 0019 2.9.0019 0018 0018 .0017 .0016 .0016 .0015 0015 0014 0014 3.0 0013 .0013 0013 .0012 0012 0011 .0011 0011 0010 0010 3.1.0010 0009 0009 .0009 0008 0008 0008 0008 0007 .0007 3.20007 0007 .0006 .0006 0006 .0006 .0006 0005 0005 0005 3.30005 0005 .0005 .0004 0004 0004 0004 0004 0004 0003 3.4 0003 0003 .0003 .0003 0003 .0003 .0003 0003 0003 0002Explanation / Answer
1) P(Z > 1.96) = 0.0250
2) P(Z > -1.96) = 1 - P(Z < -1.96) = 1 - P(Z > 1.96) = 1 - 0.0250 = 0.9750
3) P(-0.65 < Z < 2.65) = P(Z < 2.65) - P(Z < -0.65)
= [1 - P(Z > 2.65)] - [P(Z > 0.65)]
= 1 - 0.0040 - 0.2578
= 0.7382
4) P(Z < A) = 0.9951
or, 1 - P(Z > A) = 0.9951
or, P(Z > A) = 0.0049
or, A = 2.58
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