I need help with this please A random sample of size 81 is taken from a normal population having a mean of 85 and a standard deviation of 4. Asecond random sample of size 36 is taken from a different normal population having a mean of 80 and a standarddeviation of 6. Find the probability that the sample mean computed from the 81 measurements will exceed thesample mean computed from the 36 measurements by at least 3.4 but less than 5.7. Assume the difference of themeans to be measured to the nearest tenth.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 CurveAreas under the Normal Curve名.00.01.02.03.04.05.06.07.08.09社-3.3 0.0005-3.2-3.4 0.0003 0.0003 0.0003 0.00030.0005 0.0005 0.00040.0007 0.0007 0.0006 0.00060.0003-3.1 0.0010 0.0009 0.0009-3.0 0.0013 0.0013 0.00130.0019-2.90.00180.0018-0.020.0003 0.00030.0003 0.0002 -3.40.00030.0004 0.0004 0.0004 0.0004 0.0004 0.0003 -3.30.0006 0.0006 0.0006 0.00050.0005 0.0005 -3.20.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 -3.10.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 -3.00.00170.00160.00160.0015 0.0015 0.0014 0.0014-2.8 0.0026 0.0025 0.0024 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 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 -2.50.00800.0075 0.00730.0069 0.0068-2.4 0.00820.00660.00780.00710.0064 -2.4-2.3 0.0107 0.0104 0.0102 0.0099 0.00960.0094 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 0.0116 0.0113 0.0110 -2.2-2.1 0.0179 0.0174 0.0170 0.0166 0.0162 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 -2.00.02870.0274 0.0268-1.90.0262 0.02560.02810.0250 0.0244 0.0239 0.0233 -1.9-1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 -1.8-1.70.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 -1.7-1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 -1.6-1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 -1.50.0793 0.0778-1.40.0764 0.07490.08080.0735 0.0721 0.0708 0.0694 0.0681 -1.4-1.3 0.0968 0.0951 0.0934 0.0918 0.09010.0885 0.0869 0.0853 0.0838 0.0823 -1.3-1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.10200.1003 0.0985 -1.2-1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 -1.1-1.0 0.1587 0.1562 0.1539 0.1515 0.14920.1469 0.1446 0.1423 0.1401 0.1379 -1.0-0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 -0.9-0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.8-0.7 0.2420 0.2389 0.2358 0.2327 0.2296 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 0.2451 -0.6-0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.28770.2843 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 0.3594 0.3557 0.3520 0.3483 -0.3-0.2 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 -0.10.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.47210.4681 0.4641 -0.0.00.01.02.03.04.06.07.08.09.0500.00.30.4-2.92.8田.00.01.02.03.040.5000 0.5040 0.5080 0.5120 0.51600.1 0.5398 0.5438 0.54780.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.10.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.20.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.30.65540.67000.6591 0.6628 0.66640.68080.6736 0.67720.6844 0.6879 0.40.5 0.6915 0.6950 0.69850.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.50.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.60.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.70.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.80.90.82640.81590.82380.82890.81860.83150.82120.8340 0.8365 0.8389 0.91.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.01.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 1.11.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.21.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.31.4 0.91920.9236 0.9251 0.92650.9306 0.93190.9207 0.92220.9279 0.92921.41.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.94180.9429 0.9441 1.51.6 0.9452 0.9463 0.9474 0.9484 0.94950.9515 0.9525 0.9535 0.9545 1.61.70.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.71.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.81.9 0.97130.97260.9738 0.97440.9756 0.97610.97191.90.97320.97500.97672.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.02.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.12.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 2.22.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 2.32.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.42.50.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.52.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.62.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.70.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.82.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.99862.90.99863.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.03.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 3.13.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.23.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.3.05.07.06.08.090.5199 0.5239 0.5279 0.5319 0.5359 0.00.95053.40.99972A2.000.9997.010.9997.020.9997.030.9997.040.9997.050.9997.060.9997.070.99970.99983.4.08.09Z

Let X= The rv that denotes the first normal populationSample size, Mean, Sd, Let Y= The rv that…

A random sample of size 81 is taken from a normal population having a mean of 85 and a standard deviation of 4. A second random sample of size 36 is taken from a different normal population having a mean of 80 and a standard deviation of 6. Find the probability that the sample mean computed from the 81 measurements will exceed the sample mean computed from the 36 measurements by at least 3.4 but less than 5.7. Assume the difference of the means to be measured to the nearest tenth. 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.)