The distribution of heights of a certain breed of terrier has a mean of 71 centimeters and a standard deviation of 10 centimeters, whereas the distribution of heights of a certain breed of poodle has a mean of 28 centimeters with a standard deviation of 6 centimeters. Assuming that the sample means can be measured to any degree of accuracy, find the probability that the sample mean for a random sample of heights of 64 terriers exceeds the sample mean for a random sample of heights of 100 poodles by at most 44.2 centimeters. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. The probability is ☐ (Round to four decimal places as needed.) Areas under the Normal Curve Area Areas under the Normal Curve .03 .04 -1.2 -1.1 0.3015 2 .00 .01 .02 -3.4 0.0003 0.0003 0.0003 0.0003 0.0003 -3.3 0.0005 0.0005 0.0005 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 0.0005 0.0005 0.0005 -3.2 0.0006 -3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 -3.1 0.0007 -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 0.0024 0.0023 0.0023 0.0022 0.0021 0.0019 0.0021 -2.8 0.0020 0.0035 0.0033 0.0031 0.0030 0.0029 -2.7 0.0027 0.0034 0.0032 0.0028 0.0026 -2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036 -2.6 -2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 -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 0.0104 0.0099 0.0102 0.0091 0.0096 0.0094 0.0087 0.0089 0.0084 -2.3 -2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 -2.2 -2.1 0.0179 0.0166 0.0162 0.0158 0.0154 0.0150 0.0143 -2.1 0.0174 0.0170 0.0146 -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 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 0.0281 -1.9 0.0274 0.0359 -1.8 0.0344 0.0351 0.0336 0.0329 0.0307 0.0322 0.0301 0.0314 0.0294 -1.8 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 -1.7 0.0392 0.0384 0.0375 0.0367 -1.7 -1.6 0.0548 0.0516 0.0537 0.0465 0.0526 0.0455 -1.6 0.0505 0.0495 0.0485 0.0475 -1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 -1.5 0.0808 0.0793 0.0764 -1.4 0.0721 0.0708 0.0778 0.0681 0.0749 -1.4 0.0735 0.0694 -1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 -1.3 0.1131 0.1151 0.1112 0.1093 0.1056 0.1075 0.1038 0.1003 0.0985 -1.2 0.1020 0.1335 0.1314 0.1357 0.1251 0.1292 0.1271 0.1230 0.1210 0.1190 -1.1 0.1170 0.1539 0.1423 -1.0 0.1587 0.1562 0.1515 0.1492 0.1469 0.1446 0.1379 0.1401 -1.0 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 -0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.2389 -0.7 0.2420 0.2266 0.2358 0.2236 0.2327 0.2296 0.2206 0.2177 -0.6 0.2743 0.2709 0.2643 0.2578 0.2546 0.2514 0.2483 0.2676 0.2611 -0.5 0.3085 0.3050 0.2946 0.2912 0.2981 0.2810 0.2877 0.2843 -0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 -0.3 0.3783 0.3745 0.3707 0.3632 0.3821 0.3669 0.3594 0.3557 0.3520 -0.2 0.4207 0.4090 0.4168 0.4129 0.4052 0.4013 0.3974 0.3936 0.3897 0.4602 0.4522 0.4483 0.4443 -0.1 0.4364 0.4562 0.4325 0.4404 0.4286 0.4960 0.4801 -0.0 0.4721 0.5000 0.4920 0.4880 0.4840 0.4761 0.4681 .00 .01 .02 .03 .04 .05 .06 .07 .08 .05 .06 .07 .08 .09 Z .00 0.0003 0.0003 0.0003 0.0003 0.0002 -3.4 0.0 0.1 0.0004 0.0006 0.2 0.3 0.4 .01 .02 .03 .04 .05 .06 .07 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.0 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.1 0.6103 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6141 0.2 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6480 0.6406 0.6443 0.3 0.6517 0,6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.4 .08 .09 名 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.6 -2.7 0.7 0.7257 0.7580 0.8 0.7881 0.9 0.8159 1.0 0.8413 0.9726 0.7291 0.7324 0.7357 0.7611 0.7673 0.7642 0.7910 0.7939 0.7967 0.8186 0.8212 0.8238 0.8438 0.8461 0.8485 0.8508 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.9066 0.9099 1.3 0.9131 0.9032 0.9049 0.9082 0.9115 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 1.5 0.9345 0.9357 0.9370 0.9332 0.9382 0.9394 0.9406 0.9463 0.9505 1.6 0.9515 0.9452 0.9474 0.9484 0.9495 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 1.8 0.9656 0.9664 0.9641 0.9649 0.9671 0.9678 1.9 0.9713 0.9719 0.9732 0.9738 0.9744 0.5 0.7389 0.7422 0.7454 0.7486 0.7549 0.7517 0.6 0.7794 0.7823 0.7852 0.7704 0.7 0.7734 0.7764 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.8 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 0.9 0.8531 0.8554 0.8577 0.8599 0.8621 1.0 0.8790 1.1 0.8810 0.8830 0.8980 0.8997 0.9015 1.2 0.9177 0.9147 0.9162 1.3 0.9292 0.9306 0.9319 1.4 0.9686 0.9750 2.0 2.1 2.2 0.9861 0.9864 0.9772 0.9783 0.9778 0.9821 0.9826 0.9830 0.9868 2.3 0.1611 -0.9 0.9893 0,9896 2.4 0.9918 0.9920 2.5 0.9938 0.9940 0.9898 0.9922 0.1894 0.1867 -0.8 0.2148 -0.7 0.2451 -0.6 0.2776 -0.5 0.3121 0.3483 0.3859 0.4247 0.4641 -0.0 .09 -0.4 -0.3 -0.2 -0.1 2 ▲ B' \' C']' σ' 2.6 0.9957 0.9927 0.9929 0.9943 0.9945 0.9946 0.9959 0.9960 0.9931 0.9429 0.9418 0.9441 1.5 0.9525 0.9535 0.9545 1.6 0.9616 0.9625 0.9633 1.7 0.9699 0.9693 0.9706 1.8 1.9 0.9756 0.9761 0.9767 0.9788 2.0 0.9798 0.9803 0.9793 0.9817 0.9808 0.9812 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.1 0.9884 0.9887 0.9871 0.9875 0.9878 0.9881 0.9890 2.2 0.9913 0.9901 0.9904 0.9906 0.9909 0.9911 0.9925 0.9932 0.9934 0.9916 2.3 0.9936 2.4 ¡Ai --‹ ›0 = 0 2.7 2.8 2.9 3.4 2 .00 0.9941 0.9956 0.9953 0.9955 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9974 0.9976 0.9975 0.9977 0.9977 0.9979 0.9978 0.9981 0.9982 0.9982 0.9983 0.9984 0.9985 0.9986 2.9 0.9984 0.9985 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 0.9993 0.9991 0.9991 0.9992 0.9992 0.9991 0.9993 3.1 0.9992 0.9992 3.2 0.9993 3.2 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 0.9995 0.9995 3.3 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 0.9996 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 .01 .02 .03 .04 0.9948 0.9949 0.9951 0.9952 2.5 0.9961 0.9962 0.9963 0.9964 2.6 0.9972 0.9973 0.9974 2.7 0.9979 0.9980 0.9981 2.8 0.9986 0.9997 3.3 3.4 .05 .06 .07 .08 .09