Table 16.3.1 , at the bottom of this appendix, gives the proportion, P , of the area under a normal distribution curve that lies to the right of a deviation, z \[z = \frac {X -\mu} {\sigma} \nonumber\] where X is the value for which the deviation is defined, \(\mu\) is the distribution’s mean value and \(\sigma\) is the distribution’s standard deviation. For example, the proportion of the area under a normal distribution to the right of a deviation of 0.04 is 0.4840 (see entry in red in the table), or 48.40% of the total area (see the area shaded blue in Figure 16.3.1 ). The proportion of the area to the left of the deviation is 1 – P . For a deviation of 0.04, this is 1 – 0.4840, or 51.60%. Figure 16.3.1 . Normal distribution curve showing the area under a curve greater than a deviation of +0.04 ( blue ) and with a deviation less than –0.04 ( green ). When the deviation is negative—that is, when X is smaller than \(\mu\)—the value of z is negative. In this case, the values in the table give the area to the left of z . For example, if z is –0.04, then 48.40% of the area lies to the left of the deviation (see area shaded green in Figure 16.3.1 . To use the single-sided normal distribution table, sketch the normal distribution curve for your problem and shade the area that corresponds to your answer (for example, see Figure 16.3.2 , which is for Example 4.4.2 ). This divides the normal distribution curve into three regions: the area that corresponds to our answer (shown in blue ), the area to the right of this, and the area to the left of this. Calculate the values of z for the limits of the area that corresponds to your answer. Use the table to find the areas to the right and to the left of these deviations. Subtract these values from 100% and, voilà, you have your answer. 0 1 2 3 4 5 6 7 8 9 10 z 0.000000 0.0100 0.02000 0.0300 0.04000 0.0500 0.06000 0.0700 0.08000 0.0900 0.0 0.500000 0.4960 0.49200 0.4880 0.48400 0.4801 0.47610 0.4721 0.46810 0.4641 0.1 0.460200 0.4562 0.45220 0.4483 0.44430 0.4404 0.43650 0.4325 0.42860 0.4247 0.2 0.420700 0.4168 0.41290 0.4090 0.45020 0.4013 0.39740 0.3396 0.38970 0.3859 0.3 0.382100 0.3783 0.37450 0.3707 0.36690 0.3632 0.35940 0.3557 0.35200 0.3483 0.4 0.344600 0.3409 0.33720 0.3336 0.33000 0.3264 0.32280 0.3192 0.31560 0.3121 0.5 0.308500 0.3050 0.30150 0.2981 0.29460 0.2912 0.28770 0.2843 0.28100 0.2776 0.6 0.274300 0.2709 0.26760 0.2643 0.26110 0.2578 0.25460 0.2514 0.24830 0.2451 0.7 0.242000 0.2389 0.23580 0.2327 0.22960 0.2266 0.22360 0.2206 0.21770 0.2148 0.8 0.211900 0.2090 0.20610 0.2033 0.20050 0.1977 0.19490 0.1922 0.18940 0.1867 0.9 0.184100 0.1814 0.17880 0.1762 0.17360 0.1711 0.16850 0.1660 0.16350 0.1611 1.0 0.158700 0.1562 0.15390 0.1515 0.14920 0.1469 0.14460 0.1423 0.14010 0.1379 1.1 0.135700 0.1335 0.13140 0.1292 0.12710 0.1251 0.12300 0.1210 0.11900 0.1170 1.2 0.115100 0.1131 0.11120 0.1093 0.10750 0.1056 0.10380 0.1020 0.10030 0.0985 1.3 0.096800 0.0951 0.09340 0.0918 0.09010 0.0885 0.08690 0.0853 0.08380 0.0823 1.4 0.080800 0.0793 0.07780 0.0764 0.07490 0.0735 0.07210 0.0708 0.06940 0.0681 1.5 0.066800 0.0655 0.06430 0.0630 0.06180 0.0606 0.05940 0.0582 0.05710 0.0559 1.6 0.054800 0.0537 0.05260 0.0516 0.05050 0.0495 0.04850 0.0475 0.04650 0.0455 1.7 0.046600 0.0436 0.04270 0.0418 0.04090 0.0401 0.03920 0.0384 0.03750 0.0367 1.8 0.035900 0.0351 0.03440 0.0336 0.03290 0.0322 0.03140 0.0307 0.03010 0.0294 1.9 0.028700 0.0281 0.02740 0.0268 0.02620 0.0256 0.02500 0.0244 0.02390 0.0233 2.0 0.022800 0.0222 0.02170 0.0212 0.02070 0.0202 0.01970 0.0192 0.01880 0.0183 2.1 0.017900 0.0174 0.01700 0.0166 0.01620 0.0158 0.01540 0.0150 0.01460 0.0143 2.2 0.013900 0.0136 0.01320 0.0129 0.01250 0.0122 0.01190 0.0116 0.01130 0.0110 2.3 0.010700 0.0104 0.01020 NaN 0.00964 NaN 0.00914 NaN 0.00866 NaN 2.4 0.008200 NaN 0.00776 NaN 0.00734 NaN 0.00695 NaN 0.00657 NaN 2.5 0.006210 NaN 0.00587 NaN 0.00554 NaN 0.00523 NaN 0.00494 NaN 2.6 0.004660 NaN 0.00440 NaN 0.00415 NaN 0.00391 NaN 0.00368 NaN 2.7 0.003470 NaN 0.00326 NaN 0.00307 NaN 0.00289 NaN 0.00272 NaN 2.8 0.002560 NaN 0.00240 NaN 0.00226 NaN 0.00212 NaN 0.00199 NaN 2.9 0.001870 NaN 0.00175 NaN 0.00164 NaN 0.00154 NaN 0.00144 NaN 3.0 0.001350 NaN NaN NaN NaN NaN NaN NaN NaN NaN 3.1 0.000968 NaN NaN NaN NaN NaN NaN NaN NaN NaN 3.2 0.000687 NaN NaN NaN NaN NaN NaN NaN NaN NaN 3.3 0.000483 NaN NaN NaN NaN NaN NaN NaN NaN NaN 3.4 0.000337 NaN NaN NaN NaN NaN NaN NaN NaN NaN 3.5 0.000233 NaN NaN NaN NaN NaN NaN NaN NaN NaN 3.6 0.000159 NaN NaN NaN NaN NaN NaN NaN NaN NaN 3.7 0.000108 NaN NaN NaN NaN NaN NaN NaN NaN NaN 3.8 0.000072 NaN NaN NaN NaN NaN NaN NaN NaN NaN 3.9 0.000048 NaN NaN NaN NaN NaN NaN NaN NaN NaN 4.0 0.000032 NaN NaN NaN NaN NaN NaN NaN NaN NaN