The heights of 2000 students are normally distributed with a mean of 167.5 centimeters and a standard deviation of 7.4 centimeters. Assuming that the heights are recorded to the nearest? half-centimeter, how many of these students would be expected to have heights ?

(a) less than 153.0 ?centimeters? ?

(b) between 164.5 and 175.0 centimeters? inclusive? ?

(c) equal to 170.0 ?centimeters? ?

(d) greater than or equal to 185.0 ?centimeters?

\fA B C D F F G H K Z 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0 0.5 0.504 .508 .512 .516 0.5199 0.5239 0.5279 0.5319 0.5359 0.1 0.5398 0.5438 0.5478 .5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.2 0.5793 0.5832 0.5871 0.591 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.3 0.6179 0.6217 0.6255 0.629 0.6331 0.6368 0.640 0.6443 0.648 0.6517 0.4 0.6554 0.6591 0.6628 0.6664 0.67 0.6736 0.6772 0.6808 0.6844 0.6879 0.6915 0.695 0.6985 0.7019 0.7054 0.708 0.7123 0.7157 0.719 0.7224 0.6 0.7257 0.7291 0.7324 0.7357 .7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 0.758 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 10 0.8 0.7881 0.791 .7939 0.7967 .7995 0.8023 .8051 .8078 .8106 .8133 11 0.S 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.834 0.8365 0.838 12 0.8413 0.8438 0.8461 0.8485 .8508 0.8531 .8554 0.8577 0.8599 0.8621 13 1.1 0.8643 0.866 0.8686 0.8708 0.8729 0.874 0.877 0.879 0.881 0.883 14 1.2 .8849 .8869 .8888 0.8907 0.8925 .8944 .8962 .898 0.8997 0.9015 15 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 16 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9305 0.9319 17 1.5 0.9332 0.9345 0.9357 0.937 0.9382 0.9343 0.9406 0.9418 0.9429 0.9441 18 1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 19 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 20 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 21 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.975 0.9756 0.9761 0.9767 22 2 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 23 2.1 0.9821 0.9826 0.983 0.9834 0.9838 0.9842 0.9846 0.985 0.9854 0.9857 24 2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.989 25 2.3 0.9893 .9896 8686'0 0.9901 .9904 .9906 0.990 0.9911 0.9913 0.9916 26 2.4 0.9918 0.992 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 27 2.5 0.9938 0.994 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 28 2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.996 0.9961 0.9962 0.9963 0.9964 29 2.7 0.9965 0.9966 0.9967 0.996 0.9969 0.997 0.9971 0.9972 0.9973 0.9974 30 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.998 0.9981 31 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 .9986 32 3 0.9987 0.9987 0.9987 0.9988 0.998 0.998 0.998 0.9989 0.999 0.999 33 3.1 .999 0.9991 0.9991 0.9991 0.9992 .9992 0.9992 0.9992 0.9993 0.9993 34 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 0.9995 35 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.999 0.9997 36 3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998