Question

Round to 2 decimal places

Table # 1

Table # 2

Find the value of z if the area under a standard normal curve (a) to the right of z is 0.3974; (b) to the left of z is 0.0985 (c) between 0 and z, with z > 0, is 0.4812, and (d) between -z and z, with z>0, is 0.9476 lick here to view page 1 of the standard normal distribution table le reas under the Normal Curve ,00 01 02 .03 04 05 06 07 08 09 -3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0,0003 0,0003 0,0002.4 -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 -2.9 0.0019 0-0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014-2.9 -2.8 0,0026 0,0025 00024 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 0.0026-2.7 2.6 0,0047 0,0045 0.0044 0.0043 000 0,0040 0.0039 0,0038 0,0037 0.0036-2.6 -2.5 0.0062 0.000 0.0059 0.0057 0.0055 0.005-1 0.0052 0.0051 0.0019 0.0018-2.5 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 0.010 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 0.01 16 0.01 13 0.01 10-2.2 2.1 0,0179 0.0174 0,0170 0.0166 0,012 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 0,028 0.0274 0.0268 0.0262 0.0256 0.0250 0,0244 0.0239 0.02331.9 18 0.0350 0,0351 0.0344 0.0336 0.0320 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 6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455-1.6 5 0.0GG8 0.0655 0.0643 0.0630 0.0618 0.0G 0.0594 0.0582 0.0571 0.059-15 1.4 0.0808 0,0793 0.0778 0.0764 0,0749 0.0735 0.0721 0,0708 0,069 0,068 1.4 3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0860 0.0853 0.0838 0.0823 -1.3 1.2 0.15 0.1131 0.2 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 0.11701.1 .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 0.172 0.1736 0.171 0.1685 0.1660 0.1635 0.16110.9 0.8 0.2119 0.2090 0.206 0.2033 0.200 0.1977 0.1949 0.1922 0.1894 0.1867 -0.8 0.7 0.2420 0.2389 0.2358 0.2327 0.2206 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 0.24510.6 0.5 0.3085 0.3050 0.3015 0.298 0.294G 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 0.359 0.3557 0.3520 0.34830.3 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 02 .03 04 05 06 07 08 09 Areas nder the Normal Curve uestion Hel print- z 01 .02 .07 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 05319 0.5359 0.0 0.1 0.5398 0.5438 0.3478 0.5317 0.5557 0.3396 0.3636 0.3675 0.5714 0 3753 0.1 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 06103 0.6141 0.2 0.3 0.6179 0.6217 0.6255 06293 06331 0.6368 0.6406 0.6143 06180 0.6517 0.3 0.4 0.6554 0.6591 0.6628 06664 06700 06736 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 08023 0.8051 0.8078 08106 08133 0.8 0.9 0.8159 0.8186 0.8212 08238 08264 0.8289 0.8315 0.8340 0.8365 0 8389 0.9 1.0 0.8413 0.8438 0.8461 08485 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 08810 0.8830 1.1 1.2 0.8849 0.8869 0.8888 08907 0.8925 0.8944 0.8962 0880 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 09382 0.9391 0.906 0.918 09129 09441 1.5 .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 0.955 0.9564 09573 0.9582 0.9591 0.9 0.9608 0.9616 0.9625 09633 1.7 .8 0.961 0.9649 0.9656 0.966 0.9671 0.9678 0.9686 0.9693 0.9699 0.706 1.8 .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 09887 0.9800 2.2 2.3 0.9893 0.9896 0.9898 0.990 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 0.991 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 0.9T0 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 0.991 0.9991 0.9992 0.9992 0.9992 0.9092 0.9993 0.9993 3.1 3.2 09993 0,9993 0.9991 0.9991 0.9991 09991 0.999 0.9995 0.9995 0.9995 3.2 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0996 0.9996 0.9996 0.9997 3.3 3.4 09997 0,9997 0.9997 0,9997 09997 09997 0,9997 0.9997 0.9997 0.9998 3.4 1 .01 .07

Answer 1

a)

P(Z > 0.3974) 1-P(Z < 0.3974)-1-Φ(0.3974)

P(Z > 0.3974)-1-0.654464

P(Z > 0.3974) 0.345536

b) $P(Z<0.0985) = \Phi(0.0985) = 0.539232$

c) $P(0\leq Z\leq z) = 0.4812$

$\Rightarrow P(Z\leq z) -P(Z<0)= 0.4812$

$\Rightarrow \Phi(z) -\Phi(0)= 0.4812$

$\Rightarrow \Phi(z) -0.5= 0.4812$

$\Rightarrow \Phi(z)= 0.9812$

$\Rightarrow z= \Phi^{-1}(0.9812) = 2.07919$

d) $P(-z\leq Z\leq z) = 0.9476$

$\Rightarrow P(Z\leq z) - P(Z<-z)= 0.9476$

$\Rightarrow \Phi(z) - \Phi(-z)= 0.9476$

$\Rightarrow \Phi(z) -[1 - \Phi(z)]= 0.9476$

$\Rightarrow 2\Phi(z) -1 = 0.9476$

$\Rightarrow \Phi(z)= \frac{1.9476}{2} = 0.9738$

$\Rightarrow z = \Phi^{-1}(0.9738)$

$\Rightarrow z = 1.93983$ (ans)