Suppose that the manager of a construction supply house determined from historical records that demand for sand averages 54 tons. In addition, suppose the manager determined that demand during lead time could be described by a normal distribution that has a mean of 54 and a standard deviation of 6 tons. Answer the following questions assuming that the manager is willing to accept a stockout risk of no more than 2 percent. Use Table B.2

(Round your answer to two decimal points.)

a. What value of z is appropriate?

b. How much safety stock should be held? (Round your answer to two decimal points.)

c. What reorder point should be used? (Round your answer to two decimal points.)

\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} \hline & & & & & & & & & & Page 872 \\ \hlinez & .00 & .01 & .02 & .03 & .04 & .05 & .06 & .07 & .08 & .09 \\ \hline .0 & .5000 & .5040 & .5080 & .5120 & .5160 & .5199 & .5239 & .5279 & .5319 & .5359 \\ \hline .1 & .5398 & .5438 & .5478 & .5517 & .5557 & .5596 & .5636 & .5675 & .5714 & .5753 \\ \hline .2 & .5793 & .5832 & .5871 & .5910 & .5948 & .5987 & .6026 & .6064 & .6103 & .6141 \\ \hline .3 & .6179 & .6217 & .6255 & .6293 & .6331 & .6368 & .6406 & .6443 & .6430 & .6517 \\ \hline .4 & .6554 & .6591 & .6628 & .6664 & .6700 & .6736 & .6772 & .6808 & .6844 & .6879 \\ \hline .5 & .6915 & .6950 & .6985 & .7019 & .7054 & .7088 & .7123 & .7157 & .7190 & .7224 \\ \hline .6 & .7257 & .7291 & .7324 & .7357 & .7389 & .7422 & .7454 & .7486 & .7517 & .7549 \\ \hline .7 & .7580 & .7611 & .7642 & .7673 & .7703 & .7734 & .7764 & .779 & .7823 & .7852 \\ \hline .8 & .7881 & .7910 & .7939 & .7967 & .7995 & .8023 & .8051 & .8078 & .8106 & .8133 \\ \hline 9 & .8159 & .8186 & .8212 & .8238 & .8264 & .8289 & .8315 & .8340 & .8365 & .8389 \\ \hline 1.0 & .8413 & .8438 & .8461 & .8485 & .8508 & .8531 & .8554 & .8577 & .8599 & .8621 \\ \hline 1.1 & .8643 & .8665 & .8686 & .8708 & .8729 & .8749 & .8770 & .8790 & .8810 & .8830 \\ \hline 1.2 & .8849 & .8869 & .8888 & .8907 & .8925 & .8944 & .3962 & .8980 & .8997 & .9015 \\ \hline 1.3 & .9032 & .9049 & .9066 & .9082 & .9099 & .9115 & .9131 & .9147 & .9162 & .9177 \\ \hline 1.4 & .9192 & .9207 & .9222 & .9236 & 975 & .9265 & .9279 & .9292 & .9306 & .9319 \\ \hline 1.5 & .9332 & .9345 & .9357 & .9370 & .9382 & .9394 & .9406 & .9418 & .9429 & .9441 \\ \hline 1.6 & .9452 & .9463 & .9474 & .9484 & .9495 & .9505 & .9515 & .9525 & .9535 & .9545 \\ \hline 1.7 & .9554 & .9564 & .9573 & .9582 & .9591 & .9599 & .9608 & .9616 & .9625 & .9633 \\ \hline 1.8 & .9641 & .9649 & .9656 & .9664 & .9671 & .9678 & .9686 & .9693 & .9699 & .9706 \\ \hline 1.9 & .9713 & .9719 & .9726 & .9732 & .9738 & .9744 & .9750 & .9756 & .9761 & .9767 \\ \hline 2.0 & .9772 & .977 & .97 & .97 & .9793 & .97 & .98 & .98 & .9 & .9817 \\ \hline 2.1 & .9821 & .9826 & .9830 & .9834 & .9838 & .9842 & .9846 & .9850 & .9854 & .9857 \\ \hline 2.2 & .9861 & .9864 & .9868 & .9871 & .9875 & .9878 & .9881 & .9884 & .9887 & .9890 \\ \hline 2.3 & .9893 & .9896 & 9898 & 9901 & .9904 & 9906 & 9909 & 9911 & 9913 & .9916 \\ \hline 2.4 & .9918 & .9920 & .9922 & .9925 & .9927 & 9929 & .9931 & .9932 & .9934 & .9936 \\ \hline 2.5 & .9938 & .9940 & .9941 & .9943 & .9945 & .9946 & .9948 & .9949 & .9951 & .9952 \\ \hline 2.6 & .9953 & .9955 & 9956 & .9957 & .9959 & .9960 & .9961 & .9962 & .9963 & .9964 \\ \hline 2.7 & .9965 & .9966 & .9967 & .9968 & .9969 & .9970 & .99 & .99 & .9973 & .9974 \\ \hline 2.8 & .9974 & .9975 & 9976 & 9977 & .9977 & .9978 & .9979 & .99 & .9980 & .9981 \\ \hline 2.9 & .9981 & .9982 & .9982 & .9983 & .9984 & .9984 & .9985 & .9985 & .9986 & .9986 \\ \hline 3.0 & .9987 & .9987 & 9987 & .9988 & .9988 & 9989 & .9989 & .9989 & 9990 & .9990 \\ \hline 3.1 & .9990 & 999 & 9991 & .99 & 999 & 9992 & .9992 & 9992 & .9993 & .9993 \\ \hline 3.2 & .9993 & .9993 & 9994 & .9994 & 9994 & 999 & .9994 & .9995 & .9995 & .9995 \\ \hline 3.3 & .9995 & .9995 & 9995 & .9996 & .9996 & .9996 & .9996 & 9996 & .9996 & .9997 \\ \hline 3.4 & 9997. & 9997. & 9997 & .9997 & .9997 & .9997 & 9997 & .9997 & .9997 & .9998 \\ \hline \end{tabular}