1-What is the probability that an observation on the standard normal distributio

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 between z-score 2.05 and z-score 0.08.

3-What is the probability that an observation on the standard normal distribution falls between z-score 0.08 and z-score 2.05.

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.

5- Find z-score B that satisfies the following statement. The probability that an observation on the standard normal distribution falls between z-score B and z-score B is 0.925.

Standard Normal Probabiltles Table enty Table entry for z is the area under the standard normal curve to the left of z. -3.4 0003 0003 0003 0003 0003 0003 0003 .0003 0003 0002 3.3 .0005 .0005 0005 0004 .0004 .0004 .0004 .0004 0004 .0003 -3.2 0007 0007 0006 0006 0006 0006 0006 .0005 0005 0005 3.1 .0010 .0009 0009 0009 .0008 0008 .0008 .0008 0007 0007 -3.0 0013 0013 .0013 0012 .0012 .0011 .0011 .0011 0010 0010 2.9 .0019 .0018 0018 .0017 .0016 .0016 .0015 .0015 .0014 0014 -2.8 0026 .0025 0024 0023 0023 0022 .0021 .0021 0020 0019 2.7 .0035 0034 0033 0032 0031 0030 .0029 .0028 .0027 .0026 -2.6 .0047 .0045 0044 0043 0041 0040 .0039 .0038 07 0036 2.5 0062 0060 0059 0057 0055 0054 0052 .0051 0049 0048 -2.4 .0082 0080 0078 0075 .0073 .0071 .0069 .0068 .0066 .0064 2.3 .0107 0104 0102 0099 0096 .0094 .0091 .0089 0087 0084 -2.2 0139 0136 0132 0129 0125 0122 .0119 0116 0113 0110 -2.1 .0179 .0174 .0170 .0166 .0162 .0158 .0154 .0150 .0146 .0143 -2.0 0228 .0222 0217 0212 0207 0202 .0197 0192 0188 0183 -1.9 0287 0281 .0274 0268 .0262 .02560250 244 0239 0233 1.8 .0359 0351 0344 0336 .0329 0322 .0314 .0307 0301 0294 17 .0446 0436 0427 0418 .0409 0401 0384 0375 0367 1.6 0548 0537 .0526 0516 0505 0495 0485 0475 0465 0455 -1.5 0668 0655 0643 0630 0618 0606 0594 0582 0571 0559 1.4 0808 0793 0778 0764 0749 0735 0721 0708 0694 0681 1.3 0968 0951 0934 0918 0901 0885 .0869 .0853 .0838 0823 1093.1075 1056 1038 1020 1003 0985 .1190 .1170 1401 1379 .1685 .1660 .1635 1611 1.2 1151 .1131 .1112 -1.1 135 1314 15151492 1469 1446 1423 1 1.0 1587 .1562 .1539 -0.9 1841 1814 .1788 -0.8 2119 2090 .2061 2033 2005 1977 .1949 .1922 1894 1867 -0.7 2420 2389 2358 2327 2296 2266 .2236 2206 2177 2148 -0.6 2743 2709 2676 2643 2611 2578 .2546 .2514 2483 2451 -0.5 3085 .3050 -0.4 3446 3409 3372 3336 3300 3264 3228 .3192 3156 3121 2810 2776 -0.2 4207 4168 4129 4090 4052 4013 3974 .3936 3897 3859 0.1 4602 4562 4522 4483 4443 4404 4364 4325 4286 4247 -0.0 5000 4960 4920 4880 4840 4801 4761 4721 4681 4641

Explanation / Answer

1) P(Z > -1.96) = 1 - P(Z < -1.96) = 1 - 0.025 = 0.975

2) P(-2.05 < Z < 0.08) = P(Z < 0.08) - P(Z < -2.05)

                                    = [1 - P(Z < -0.08)] - P(Z < -2.05)

                                    = 1 - 0.4681 - 0.0202

                                    = 0.5117

3) P(0.08 < Z < 2.05) = P(Z < 2.05) - P(Z < 0.08)

                                  = [1 - P(Z < -2.05)] - [1 - P(Z < -0.08)]

                                  = 1 - 0.0202 - 1 + 0.4681

                                  = 0.4479

4) P(Z < A) = 0.9951

or, 1 - P(Z < -A) = 0.9951

or, P(Z < -A) = 0.0049

or, A = 2.58

5) P(-B < Z < B) = 0.925

or, P(Z < B) - P(Z < -B) = 0.925

or, [1 - P(Z < -B)] - P(Z < -B) = 0.925

or, 1 - 2 * P(Z < -B) = 0.925

or, P(Z < -B) = 0.0375

or, B = 1.78

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