I need help with parts b,c, and d The heights of 1500 students are normally distributed with a mean of 176.5 centimeters and a standard deviation of7.2 centimeters. Assuming that the heights are recorded to the nearest half-centimeter, how many of these studentswould be expected to have heights(a) less than 159.0 centimeters?(b) between 171.5 and 186.0 centimeters inclusive?(c) equal to 178.0 centimeters?(d) greater than or equal to 192.0 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.(a) 11 student(s)(Round to the nearest whole number as needed.)(b) ☐ student(s)(Round to the nearest whole number as needed.) Areas under the Normal CurveAreas under the Normal Curvez.00.01-3.40.0003 0.0003 0.0003 0.0003-3.3 0.0005 0.0005 0.0005 0.0004-3.2 0.0007 0.0007 0.0006 0.0006-3.1 0.0010 0.0009 0.0009 0.0009-3.0 0.0013 0.0013 0.0013 0.0012-2.9 0.0019 0.0018 0.0018 0.0017-2.8 0.0026 0.0025 0.0024 0.0023-2.7 0.0035 0.0034 0.0033 0.0032-2.6 0.0047 0.0045 0.0044 0.0043-2.5 0.0062 0.0060 0.0059 0.0057-2.4 0.0082 0.0080 0.0078 0.0075-2.3 0.0107 0.0104 0.0102 0.0099.02.03.05.04.06.070.0003 0.00030.0003 0.00030.0004 0.0004 0.0004 0.00040.0006 0.0006 0.0006 0.00050.0008 0.0008 0.0008 0.00080.0012 0.0011 0.0011 0.00110.0016 0.0016 0.0015 0.00150.0023 0.0022 0.0021 0.00210.0031 0.0030 0.0029 0.0028.08.090.0003 0.0002 -3.40.0004 0.0003 -3.30.0005 0.0005 -3.2zZ.00.01.02.03.04.05.06.070.0007 0.0007 -3.10.0010 0.0010 -3.00.30.4-0.3 0.3821 0.3783 0.37452.00.010.0041 0.0040 0.0039 0.00380.0055 0.0054 0.0052 0.00510.0073 0.0071 0.0069 0.0068 0.0066 0.0064 -2.40.0096 0.0094 0.0091 0.0089 0.0087-2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113-2.1 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 -2.0-1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 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 -1.8-1.7 0.0446 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 0.05710.0559 -1.5-1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 -1.4-1.30.0968 0.0951 0.0934 0.0918 0.0901 0.0885 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 0.1020 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 0.1170 -1.1-1.0 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 0.1762 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 0.2514-0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843-0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.31920.3707 0.3669 0.3632 0.3594 0.35570.3483 -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 -0.1-0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641 -0.0.02.03.04.05.06.07.08.09Z0.0014 0.0014 -2.90.0020 0.0019 -2.80.0027 0.0026 2.70.0037 0.0036 -2.60.0049 0.0048 -2.50.50.0084 -2.30.0110 -2.20.0143 -2.12.70.2483 0.2451 -0.60.28100.2776 -0.50.31560.35200.3121 -0.4¡A2.000.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.52790.1 0.5398 0.5438 0.5478 0.5517 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 0.62550.6293 0.63310.6368 0.6406 0.6443 0.6480 0.6517 0.30.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.40.6915 0.6950 0.6985 0.7019 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 0.80.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 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 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.41.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.51.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.61.7 0.9554 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 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 1.92.0 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 0.98780.9881 0.9884 0.9887 0.9890 2.22.30.9893 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 2.42.5 0.9938 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 2.60.9965 0.9966 0.99670.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.72.80.9974 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 0.9986 0.9986 2.93.0 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 0.99920.9992 0.9992 0.9993 0.9993 3.13.2 0.99930.9993 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 3.33.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 3.4.01.02.03.04.05.06.07.08.09.08.090.5319 0.5359 0.02Z

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No. of students, The students' heights have a normal distribution.Mean height,  cmsStandard…