A random sample of size n = 54 is taken from a finite population of size N = 447 with mean ? = 245 and variance ? 2 = 340. [You may find it useful to reference the z table .]
a-1. Is it necessary to apply the finite population correction factor?
multiple choice
a-2. Calculate the expected value and the standard error of the sample mean.(Round "expected value" to a whole number and "standard error" to 4 decimal places.)
b. What is the probability that the sample mean is less than 231? (Round final answer to 4 decimal places.)
c. What is the probability that the sample mean lies between 236 and 255? (Round final answer to 4 decimal places.)
TABLE 1 Standard Normal Curve Areas Entries in this table provide cumulative probabilities, that is, the area P (ZS - 2) under the curve to the left of -z. For example, P(Z S -1.52) = 0.0643. -Z 0 Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0000 0.0000 0.0000 0.0000 -3.9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 -3.8 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 -3.7 0.0001 0.0001 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 -3.6 -3.5 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 -3. 0.0005 0.0004 0.0004 0.0004 0.0003 -3.3 0.0005 0.0005 0.0004 0.0004 0.0004 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005 -3.2 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 -3.1 0.0012 0.0010 0.0013 0.0013 0.0011 0.0011 0.0010 -3.0 0.0013 0.0012 0.0011 0.0014 0.0014 -2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 -2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 0.0028 0.0027 0.0026 -2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0038 0.0037 0.0036 -2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0049 0.0048 -2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0069 0.0068 0.0066 0.0064 -2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 -2.3 0.0107 0.0104 0.0136 0.0132 0.0129 0.0125 0.0122 0.01 19 0.0116 0.0113 0.01 10 -2.2 0.0139 0.0143 -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 0.0183 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 -1. 0.0322 0.0301 0.0294 0.0359 0.0351 0.0344 0.0336 0.0329 0.0314 0.0307 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 0.0446 0.0436 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 -1.6 0.0571 0.0559 -1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0681 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 0.0968 0.0951 0.1131 0. 1093 0.1003 0.0985 0.1151 0.1112 0.1075 0.1056 0.1038 0.1020 0.1170 1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1401 0.1379 10 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 -0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.7 0.2389 0.2358 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 0.2420 0.2327 0.2451 -0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 -0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 -0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 0.3594 0.3557 0.3520 0.3483 -0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.4207 0.4052 0.3936 0.3859 -0.2 0.4168 0.4129 0.4090 0.4013 0.3974 0.3897 -0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641 -0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.0 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.1 0.5398 0.6026 0.6064 0.6103 0.6141 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.3 0.6879 0.4 0.6591 0.6700 0.6736 0.6844 0.6554 0.6628 0.6664 0.6772 0.6808 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.5 0.6915 0.6950 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 0.8485 0.8508 0.8554 0.8599 0.8621 1.0 0.8413 0.8438 0.8461 0.8531 0.8577 0.8810 0.8830 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.9015 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 0.9332 0.9345 0.9495 0.9505 0.9535 0.9545 0.9452 0.9463 0.9474 0.9484 0.9515 0.9525 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 20 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 0.9772 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 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.4 0.9918 0.9920 0.9952 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.6 0.9953 0.9955 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.7 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.8 0.9974 0.9975 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 0.9990 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 0.9995 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9996 0.9997 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 3.4 0.9998 0.9998 0.9998 3.5 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.6 0.9998 0.9998 3.7 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.8 1.0000 39 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 Source: Probabilities calculated with Excel
