A Las Vegas supermarket bakery must decide how many wedding cakes to prepare for the upcoming weekend. Cakes cost $55 each to make and they sell for $64 each. The price of leftover wedding cakes is reduced by 50% on Mondays to clear out inventory. Demand for the weekend is normally distributed with a mean of 109 and a standard deviation of 13.

What is the optimal number of wedding cakes to stock on the weekend?

My real question is, how do I figure out if I will have a positive or negative z value given the problem and the z-table below? This is the z-table allowed on the exam. I already know the answer to this problem. It is highlighted in bright yellow at the bottom. For whoever answers this problem please focus on the z-value. Based on the given problem and the provided z-chart. How do you figure out the z-value by hand? How do you know it is negative?

\begin{tabular}{|c|c|c|c|} \hline \multicolumn{4}{|c|}{\begin{tabular}{l} What is the optimal number of \\ wedding cakes to stock on the \\ weekend? \end{tabular}} \\ \hline \multicolumn{4}{|c|}{ Step 1: List out Variables } \\ \hline \multicolumn{2}{|c|}{ Demand } & \multicolumn{2}{|c|}{109} \\ \hline \multicolumn{2}{|c|}{ Standard Dev ()} & \multicolumn{2}{|c|}{13} \\ \hline \multicolumn{2}{|c|}{ Cost of Cake } & $ & 55.00 \\ \hline \multicolumn{2}{|c|}{ Selling Price } & $ & 64.00 \\ \hline \multicolumn{2}{|c|}{ Reduced Price 50%} & $ & 32.00 \\ \hline \multicolumn{4}{|c|}{ Step 2: Find Cs \& Co } \\ \hline \multicolumn{2}{|c|}{ Cs = Selling-Cost } & & 9 \\ \hline \multicolumn{2}{|c|}{ Co = Cost-Salvage } & & 23 \\ \hline \multicolumn{2}{|c|}{Cs/(Cs+Co)} & & 2813 \\ \hline \multicolumn{4}{|c|}{ Step 2: Find z-score and D+zo } \\ \hline z-score & \multicolumn{3}{|c|}{-0.58} \\ \hlinez & \multicolumn{3}{|c|}{-7.5400} \\ \hline D+z & \multicolumn{3}{|c|}{101.4600} \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} \hline \multicolumn{11}{|c|}{ Area from positive z-value to left tail } \\ \hline z-values & 0.00 & 0.01 & 0.02 & 0.03 & 0.04 & 0.05 & 0.06 & 0.07 & 0.08 & 0.09 \\ \hline 0.00 & 0.5000 & 0.5040 & 0.5080 & 0.5120 & 0.5160 & 0.5199 & 0.5239 & 0.5279 & 0.5319 & 0.5359 \\ \hline 0.10 & 0.5398 & 0.5438 & 0.5478 & 0.5517 & 0.5557 & 0.5596 & 0.5636 & 0.5675 & 0.5714 & 0.5753 \\ \hline 0.20 & 0.5793 & 0.5832 & 0.5871 & 0.5910 & 0.5948 & 0.5987 & 0.6026 & 0.6064 & 0.6103 & 0.6141 \\ \hline 0.30 & .6179 & 0.6217 & 0.6255 & 0.6293 & 0.6331 & 0.6368 & 0.6406 & 0.6443 & 0.6480 & 0.6517 \\ \hline 0.40 & 0.6554 & 0.6591 & 0.6628 & 0.6664 & 0.6700 & 0.6736 & 0.6772 & 0.6808 & 0.6844 & 0.6879 \\ \hline 0.50 & 0.6915 & 0.6950 & 0.6985 & 0.7019 & 0.7054 & 0.7088 & 0.7123 & 0.7157 & 0.7190 & 0.7224 \\ \hline 0.60 & 0.7257 & 0.7291 & 0.7324 & 0.7357 & 0.7389 & 0.7422 & 0.7454 & 0.7486 & 0.7517 & 0.7549 \\ \hline 0.70 & .7580 & 0.7611 & 0.7642 & 0.7673 & 0.7704 & 0.7734 & 0.7764 & 0.7794 & 0.7823 & 0.7852 \\ \hline 0.80 & .7881 & .7910 & 0.7939 & 0.7967 & 0.7995 & 0.8023 & 0.8051 & 0.8078 & 0.8106 & 0.8133 \\ \hline 0.90 & 0.8159 & 0.8186 & 0.8212 & 0.8238 & 0.8264 & 0.8289 & 0.8315 & 0.8340 & & 0.8389 \\ \hline 1.00 & 0.8413 & 0.8438 & 0.8461 & 0.8485 & 0.8508 & 0.8531 & 0.8554 & 0.8577 & 0.8 & 0.8621 \\ \hline 1.10 & .8643 & 0.8665 & 0.8686 & 0.8708 & 0.8 & & 0.8770 & 0.8790 & & 0.8830 \\ \hline 1.20 & 8849 & 0.88 & 0.8888 & 0.89 & 0.8 & & & & & \\ \hline 1.30 & 9032 & 0.90 & 0.90 & 0.9 & 0.9 & & 0.9131 & 0.91 & & .9177 \\ \hline 1.40 & 0.9192 & 0.9207 & 0.9222 & 0.9236 & 0.9251 & 0.9265 & 0.9279 & 0.9292 & 0.9 & 0.9319 \\ \hline 1.50 & .9332 & 0.9345 & 0.9357 & 0.93 & 0.9 & & 0.9406 & 0.9418 & 0.9 & 0.9441 \\ \hline 1.60 & 9452 & 0.94 & & & & & & & & 0.9545 \\ \hline 1.70 & 0.9554 & & & & & & & & & 0.9633 \\ \hline 1.80 & 0.9641 & 0.9649 & 0.9656 & 0.96 & 0.9 & 0.9 & 0.9686 & 0.9693 & 0.9 & 0.9706 \\ \hline 1.90 & 0.9713 & 0.9719 & 0.9726 & 0.9732 & 0.9738 & 0.9744 & 0.9750 & 0.9756 & 0.9 & 0.9767 \\ \hline 2.00 & 0.9772 & 0.9778 & 0.9783 & 0.97 & & & 0.9803 & & & 0.9817 \\ \hline 2.10 & 9821 & 0.9826 & 0.9830 & 0.98 & & & 0.9846 & 0.9850 & & 0.9857 \\ \hline 2.20 & 0.9861 & 0.9864 & 0.9868 & 0.9871 & 0.9 & 0.9 & 0.9881 & 0.9884 & 0.9 & 0.9890 \\ \hline 2.30 & 0.9893 & 0.9896 & 0.9898 & 0.9901 & 0.9904 & 0.9906 & 0.9909 & 0.9911 & 0.9913 & 0.9916 \\ \hline 2.40 & 0.9918 & 0.9920 & 0.9922 & 0.9925 & 0.9927 & & 0.9931 & 0.9932 & & 0.9936 \\ \hline 2.50 & 0.9938 & 0.9940 & 0.9941 & 0.99 & & & 0.9948 & 0.9949 & & 0.9952 \\ \hline 2.60 & 0.9953 & 0.9955 & 0.9956 & 0.9957 & 0.9959 & & 0.9961 & 0.9962 & 0.9963 & 0.9964 \\ \hline 2.70 & 0.9965 & 0.9966 & 0.9967 & 0.9968 & 0.9969 & 0.9970 & 0.9971 & 0.9972 & 0.9973 & 0.9974 \\ \hline 2.80 & 0.9974 & 0.9975 & 0.9976 & 0.9977 & 0.9977 & 0.9978 & 0.9979 & 0.9979 & 0.9980 & 0.9981 \\ \hline 2.90 & 0.9981 & 0.9982 & 0.9982 & 0.9983 & 0.9984 & 0.9984 & 0.9985 & 0.9985 & 0.9986 & 0.9986 \\ \hline 3.00 & 0.9987 & 0.9987 & 0.9987 & 0.9988 & 0.9988 & 0.9989 & 0.9989 & 0.9989 & 0.9990 & 0.9990 \\ \hline \end{tabular}