Answer Happy

Suppose a simple random sample of size n = 15 is obtained from a population with μ = 66 and = 18. (a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample mean? Assuming the normal model can be used, describe the sampling distribution x. (b) Assuming the normal model can be used, determine P(X < 69.2). (c) Assuming the normal model can be used, determine P(x2 67.9). Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) What must be true regarding the distribution of the population? O A. There are no requirements on the shape of the distribution of the population. OB. The population must be normally distributed. O C. The population must be normally distributed and the sample size must be large. O D. Since the sample size is large enough, the population distribution does not need to be normal. Assuming the normal model can be used, describe the sampling distribution x Normal, with = 66 and OA OB. Normal, with μ = 66 and o OC. Normal, with μ = 66 and = (b) P(x < 69.2) = (c) P(x ≥67.9) = 18 15 √18 18 √15 (Round to four decimal places as needed.) (Round to four decimal places as needed.)
7/9/22, 2:10 PM Area Z -3.4 -3.3 -3.2 -3.1 -3.0 -29 -2.8 -2.7 -2.6 -2.5 -2.4 -2.2 -2.0 -1.9 -1.8 -1.7 -1.6 -1.5 -1.4 -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 -0.0 Z 0.00 0.0003 0.0005 0.0007 0.01 0.0003 0.0005 0.0007 0.02 0.0003 0.0003 0.0005 0.0004 0.0006 0.0006 0.0009 0.0009 0.0010 0.0013 0.0013 0.0013 0.0019 0.0018 0.0018 0.0017 0.0016 0.0026 0.0025 0.0024 0.0023 0.0023 0.0035 0.0034 0.0033 0.0032 0.0031 0.0047 0.0045 0.0044 0.0043 0.0041 0.0062 0.0060 0.0059 0.0057 0.0055 0.0287 0.0281 0.0359 0.0351 0.0446 0.0436 0.0427 0.0548 0.0537 0.0526 0.0668 0.0655 0.0643 0.0808 0.0793 0.0968 0.1151 0.1357 0.1335 0.1587 0.1562 0.1539 0.0951 0.1131 0.3446 0.3821 0.4207 0.4602 0.5000 0.00 Standard Normal Distribution 0.03 0.04 0.05 0.0274 0.0268 0.0344 0.0336 0.0418 0.0516 0.0505 0.0630 0.0618 0.0778 0.0934 0.1112 0.1841 0.1814 0.1788 0.2119 0.2090 0.2061 0.2420 0.2389 0.2358 0.4562 0.4960 0.01 0.0009 0.0008 0.0012 0.0012 0.0054 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0222 0.0212 0.0207 0.0202 0.0197 0.0250 0.0228 0.0217 0.0244 0.0239 0.0314 0.0307 0.0301 0.0392 0.0384 0.0375 0.0485 0.0475 0.0594 0.0003 0.0004 0.0006 0.0764 0.0918 0.1093 0.2743 0.2709 0.2676 0.2643 0.3085 0.3050 0.3015 0.2981 0.1762 0.2033 0.2327 0.1314 0.1292 0.1271 0.1515 0.1492 Standard Normal Distribution Table (page 1) 0.0003 0.0004 0.0262 0.0256 0.0329 0.0322 0.0409 0.0401 0.1736 0.2005 0.2296 0.2611 0.2946 0.0006 0.0006 0.0008 0.0008 0.0011 0.0016 0.0015 0.0015 0.0014 0.0022 0.0021 0.0021 0.0020 0.0030 0.0029 0.0028 0.0027 0.0040 0.0039 0.0038 0.0037 0.0052 0.0051 0.0049 0.0749 0.0735 0.0001 0.0885 0.1075 0.1056 0.0495 0.0606 0.06 0.07 0.0003 0.0003 0.0004 0.0004 0.0005 0.0008 0.0011 0.0011 0.1251 0.1469 0.3409 0.3372 0.3336 0.3300 0.3264 0.3783 0.3745 0.3707 0.3669 0.3632 0.4168 0.4129 0.4090 0.4052 0.4013 0.4522 0.4483 0.4443 0.4404 0.4920 0.4880 0.4840 0.4801 0.02 0.03 0.04 0.05 0.0721 0.0869 0.1038 0.1711 0.1685 0.1977 0.1949 0.2266 0.2236 0.2578 0.2546 0.2912 0.2877 0.08 0.0003 0.0004 0.0005 0.0007 0.0010 0.0068 0.0066 0.0089 0.0087 0.0116 0.0113 0.0150 0.0146 0.0192 0.0188 0.1230 0.1210 0.1446 0.1423 0.0465 0.0582 0.0571 0.0708 0.0694 0.0853 0.1020 0.3228 0.3192 0.3594 0.3557 0.3974 0.4364 0.4761 0.06 0.0838 0.1003 0.1190 0.1401 0.09 0.0002 0.0003 0.0005 0.0007 0.0010 0.3156 0.3520 0.3936 0.3897 0.4325 0.4286 0.4721 0.4681 0.07 0.08 0.0014 0.0019 0.0026 0.0036 0.0048 0.0064 0.0084 0.0110 0.0143 0.0183 0.0233 0.0294 0.0367 0.0455 0.0559 0.0681 0.0823 0.0985 0.1660 0.1635 0.1611 0.1922 0.1894 0.1867 0.2206 0.2177 0.2148 0.2514 0.2483 0.2451 0.2843 0.2810 0.2776 0.1170 0.1379 0.3121 0.3483 0.3859 0.4247 0.4641 0.09
7/9/22, 2:10 PM N 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 N Area 0.00 0.5000 0.5398 0.5793 0.7881 0.8159 0.9332 0.9452 0.9554 0.01 0.02 0.5040 0.5080 0.5120 0.5438 0.5478 0.5160 0.5517 0.5557 0.5832 0.5871 0.5910 0.5948 0.6179 0.6217 0.6255 0.6443 0.6554 0.6591 0.6915 0.6950 0.7257 0.7291 0.7580 0.6293 0.6331 0.6368 0.6406 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7611 0.7642 0.7673 0.7704 0.7734 0.7910 0.7939 0.7967 0.7995 0.8186 0.8212 0.8238 0.8264 0.8289 0.8413 0.8438 0.8461 0.8485 0.8643 0.8665 0.8686 0.8708 0.8888 0.7764 0.7794 0.8023 0.8849 0.8869 0.8907 0.8925 0.9032 0.9049 0.9066 0.9192 0.9207 0.9222 0.9641 0.9713 0.9772 0.9821 0.9861 0.9345 0.9463 0.9474 0.9564 0.9573 0.9649 0.9656 0.9719 0.9726 0.9778 0.9783 0.9826 0.9830 0.9864 0.9868 0.9893 0.9896 0.9918 0.9920 0.9938 0.9940 0.9953 0.9955 0.9965 0.9966 0.9974 0.9981 0.9898 0.9922 0.9975 0.9976 0.9982 0.9982 0.9987 0.9987 0.9987 0.9990 0.9991 0.9993 0.9993 0.9995 0.9995 0.9997 0.9997 0.00 0.01 Standard Normal Distribution 0.03 0.04 0.05 0.9991 0.9994 0.9082 0.9236 0.9995 0.9997 0.02 0.9941 0.9943 0.9945 0.9956 0.9957 0.9959 0.9967 0.9968 0.9969 0.9977 0.9977 0.9983 0.9984 0.9901 0.9925 0.9099 0.9251 0.9788 0.9793 0.9834 0.9838 0.9871 0.9875 0.9904 0.9927 0.8508 0.8531 0.8729 0.8749 0.8944 0.9988 0.9991 0.9994 0.9996 0.9997 0.03 Standard Normal Distribution Table (page 2) 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9505 0.9515 0.9525 0.9484 0.9495 0.9582 0.9591 0.9664 0.9671 0.9732 0.9738 0.9599 0.9608 0.9616 0.9686 0.9693 0.9750 0.9756 0.9988 0.9992 0.9994 0.5199 0.5596 0.5987 0.9996 0.9997 0.04 0.06 0.07 0.5239 0.5279 0.5636 0.6026 0.9678 0.9744 0.9115 0.9131 0.9265 0.9279 0.8051 0.8315 0.9946 0.9960 0.9970 0.8554 0.8770 0.8962 0.9798 0.9803 0.9842 0.9846 0.9878 0.9881 0.9906 0.9929 0.9996 0.9997 0.05 0.08 0.5319 0.5675 0.5714 0.6064 0.6103 0.9909 0.9931 0.9989 0.9989 0.9992 0.9992 0.9994 0.9994 0.7190 0.7517 0.7823 0.8078 0.8106 0.8340 0.8365 0.8577 0.8599 0.8810 0.8997 0.8790 0.8980 0.9147 0.9292 0.6480 0.6844 0.9162 0.9306 0.9429 0.9535 0.9625 0.9699 0.9761 0.9808 0.9812 0.9850 0.9854 0.9884 0.9887 0.9911 0.9913 0.9932 0.9934 0.9948 0.9961 0.9971 0.9978 0.9979 0.9979 0.9980 0.9984 0.9985 0.9985 0.9986 0.9949 0.9951 0.9962 0.9963 0.9972 0.9973 0.9996 0.9996 0.9997 0.9997 0.06 0.07 0.09 0.5359 0.5753 0.6141 0.6517 0.6879 0.7224 0.7549 0.7852 0.8133 0.8389 0.8621 0.8830 0.90 15 0.9177 0.9319 0.9441 0.9545 0.9633 0.9706 0.9767 0.9817 0.9857 0.9890 0.9916 0.9936 0.9952 0.9964 0.9974 0.9981 0.9986 0.9989 0.9990 0.9990 0.9992 0.9993 0.9993 0.9995 0.9995 0.9995 0.9996 0.9997 0.9997 0.9998 0.08 0.09