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5.3.2: Table of Critical Values of z

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    22052
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    Table \(\PageIndex{1}\) shows z-scores, their probability (p-value), and percentage. If this table is too unwieldy, here is a PDF of a z-score table with only three columns (z-score, p-value, percent) with more than 600 rows of z-scores (instead of Table \(\PageIndex{1}\)).

    Table \(\PageIndex{1}\)- Table of z-scores, Probabilities, and Percentages
    Scores from -3.00 to -2.00 Scores from -1.99 to -1.00 Scores from -0.99 to zero Scores from 0.01 to 1.00 Scores from 1.01 to 2.00 Scores from 2.01 to 3.00
    z-Score p-value % z-Score p-value %   z-Score p-value %   z-Score p-value %   z-Score p-value %   z-Score p-value %
    -3.00 0.0014 0.14% -1.99 0.0233 2.33%   -0.99 0.1611 16.11%   0.01 0.5040 50.40%   1.01 0.8438 84.38%   2.01 0.9778 97.78%
    -2.99 0.0014 0.14% -1.98 0.0239 2.39%   -0 98 0.1635 16.35%   0.02 0.5080 50.80%   1.02 0.8461 84.61%   2.02 0.9783 97.83%
    -2.98 0.0014 0.14% -1.97 0.0244 2.44%   -0.97 0.1660 16.60%   0.03 0.5120 51.20%   1.03 0.8485 84.85%   2.03 0.9788 97.88%
    -2.97 0.0015 0.15% -1.96 0.0250 2.50%   -0.96 0.1685 16.85%   0.04 0.5160 51.60%   1.04 0.8508 85.08%   2.04 0.9793 97.93%
    -2.96 0.0015 0.15% -1.95 0.0256 2.56%   -0.95 0.1711 17.11%   0.05 0.5199 51.99%   1.05 0.8531 85.31%   2.05 0.9798 97.98%
    -2.95 0.0016 0.16% -1.94 0.0262 2.62%   -0.94 0.1736 17.36%   0.06 0.5239 52.39%   1.06 0.8554 85.54%   2.06 0.9803 98.03%
    -2.94 0.0016 0.16% -1.93 0.0268 2.68%   -0.93 0.1762 17.62%   0.07 0.5279 52.79%   1.07 0.8577 85.77%   2.07 0.9808 98.08%
    -2.93 0.0017 0.17% -1.92 0.0274 2.74%   -0.92 0.1788 17.88%   0.08 0.5319 53.19%   1.08 0.8599 85.99%   2.08 0.9812 98.12%
    -2.92 0.0018 0.18% -1.91 0.0281 2.81%   -0.91 0.1814 18.14%   0.09 0.5359 53.59%   1.09 0.8621 86.21%   2.09 0.9817 98.17%
    -2.91 0.0018 0.18% -1.90 0.0287 2.87%   -0.90 0.1841 18.41%   0.10 0.5398 53.98%   1.10 0.8643 86.43%   2.10 0.9821 98.21%
    -2.90 0.0019 0.19% -1.89 0.0294 2.94%   -0.89 0.1867 18.67%   0.11 0.5438 54.38%   1.11 0.8665 86.65%   2.11 0.9826 98.26%
    -2.89 0.0019 0.19% -1.88 0.0301 3.01%   -0.88 0.1894 18.94%   0.12 0.5478 54.78%   1.12 0.8686 86.86%   2.12 0.9830 98.30%
    -2.88 0.0020 0.20% -1.87 0.0307 3.07%   -0.87 0.1922 19.22%   0.13 0.5517 55.17%   1.13 0.8708 87.08%   2.13 0.9834 98.34%
    -2.87 0.0021 0.21% -1.86 0.0314 3.14%   -0.86 0.1949 19.49%   0.14 0.5557 55.57%   1.14 0.8729 87.29%   2.14 0.9838 98.38%
    -2.86 0.0021 0.21% -1.85 0.0322 3.22%   -0.85 0.1977 19.77%   0.15 0.5596 55.96%   1.15 0.8749 87.49%   2.15 0.9842 98.42%
    -2.85 0.0022 0.22% -1.84 0.0329 3.29%   -0.84 0.2005 20.05%   0.16 0.5636 56.36%   1.16 0.8770 87.70%   2.16 0.9846 98.46%
    -2.84 0.0023 0.23% -1.83 0.0336 3.36%   -0.83 0.2033 20.33%   0.17 0.5675 56.75%   1.17 0.8790 87.90%   2.17 0.9850 98.50%
    -2.83 0.0023 0.23% -1.82 0.0344 3.44%   -0.82 0.2061 20.61%   0.18 0.5714 57.14%   1.18 0.8810 88.10%   2.18 0.9854 98.54%
    -2.82 0.0024 0.24% -1.81 0.0352 3.52%   -0.81 0.2090 20.90%   0.19 0.5754 57.54%   1.19 0.8830 88.30%   2.19 0.9857 98.57%
    -2.81 0.0025 0.25% -1.80 0.0359 3.59%   -0.80 0.2119 21.19%   0.20 0.5793 57.93%   1.20 0.8849 88.49%   2.20 0.9861 98.61%
    -2.80 0.0026 0.26% -1.79 0.0367 3.67%   -0.79 0.2148 21.48%   0.21 0.5832 58.32%   1.21 0.8869 88.69%   2.21 0.9865 98.65%
    -2.79 0.0026 0.26% -1.78 0.0375 3.75%   -0.78 0.2177 21.77%   0.22 0.5871 58.71%   1.22 0.8838 88.38%   2.22 0.9868 98.68%
    -2.78 0.0027 0.27% -1.77 0.0384 3.84%   -0.77 0.2207 22.07%   0.23 0.5910 59.10%   1.23 0.8907 89.07%   2.23 0.9871 98.71%
    -2.77 0.0028 0.28% -1.76 0.0392 3.92%   -0.76 0.2236 22.36%   0.24 0.5948 59.48%   1.24 0.8925 89.25%   2.24 0.9875 98.75%
    -2.76 0.0029 0.29% -1.75 0.0401 4.01%   -0.75 0.2266 22.66%   0.25 0.5987 59.87%   1.25 0.8944 89.44%   2.25 0.9878 98.78%
    -2.75 0.0030 0.30% -1.74 0.0409 4.09%   -0.74 0.2297 22.97%   0.26 0.6026 60.26%   1.26 0.8562 85.62%   2.26 0.9881 98.81%
    -2.74 0.0031 0.31% -1.73 0.0418 4.18%   -0.73 0.2327 23.27%   0.27 0.6064 60.64%   1.27 0.8980 89.80%   2.27 0.9884 98.84%
    -2.73 0.0032 0.32% -1.72 0.0427 4.27%   -0.72 0.2358 23.58%   0.28 0.6103 61.03%   1.28 0.8997 89.97%   2.28 0.9887 98.87%
    -2.72 0.0033 0.33% -1.71 0.0436 4.36%   -0.71 0.2389 23.89%   0.29 0.6141 61.41%   1.29 0.9015 90.15%   2.29 0.9890 98.90%
    -2.71 0.0034 0.34% -1.70 0.0446 4.46%   -0.70 0.2420 24.20%   0.30 0.6179 61.79%   1.30 0.9032 90.32%   2.30 0.9893 98.93%
    -2.70 0.0035 0.35% -1.69 0.0455 4.55%   -0.69 0.2451 24.51%   0.31 0.6217 62.17%   1.31 0.9349 93.49%   2.31 0.9896 98.96%
    -2.69 0.0036 0.36% -1.68 0.0465 4.65%   -0.68 0.2483 24.83%   0.32 0.6255 62.55%   1.32 0.9366 93.66%   2.32 0.9898 98.98%
    -2.68 0.0037 0.37% -1.67 0.0475 4.75%   -0.67 0.2514 25.14%   0.33 0.6293 62.93%   1.33 0.9382 93.82%   2.33 0.9901 99.01%
    -2.67 0.0038 0.38% -1.66 0.0485 4.85%   -0.66 0.2546 25.46%   0.34 0.6331 63.31%   1.34 0.9099 90.99%   2.34 0.9904 99.04%
    -2.66 0.0039 0.39% -1.65 0.0495 4.95%   -0.65 0.2579 25.79%   0.35 0.6368 63.68%   1.35 0.9115 91.15%   2.35 0.9906 99.06%
    -2.65 0.0040 0.40% -1.64 0.0505 5.05%   -0.64 0.2611 26.11%   0.36 0.6406 64.06%   1.36 0.9131 91.31%   2.36 0.9909 99.09%
    -2.64 0.0042 0.42% -1.63 0.0516 5.16%   -0.63 0.2644 26.44%   0.37 0.6443 64.43%   1.37 0.9147 91.47%   2.37 0.9911 99.11%
    -2.63 0.0043 0.43% -1.62 0.0526 5.26%   -0.62 0.2676 26.76%   0.38 0.6480 64.80%   1.38 0.9162 91.62%   2.38 0.9913 99.13%
    -2.62 0.0044 0.44% -1.61 0.0537 5.37%   -0.61 0.2709 27.09%   0.39 0.6517 65.17%   1.39 0.9177 91.77%   2.39 0.9916 99.16%
    -2.61 0.0045 0.45% -1.60 0.0548 5.48%   -0.60 0.2743 27.43%   0.40 0.6554 65.54%   1.40 0.9192 91.92%   2.40 0.9918 99.18%
    -2.60 0.0047 0.47% -1.59 0.0559 5.59%   -0.59 0.2776 27.76%   0.41 0.6591 65.91%   1.41 0.9207 92.07%   2.41 0.9920 99.20%
    -2.59 0.0048 0.48% -1.58 0.0571 5.71%   -0.58 0.2810 28.10%   0.42 0.6628 66.28%   1.42 0.9222 92.22%   2.42 0.9922 99.22%
    -2.58 0.0049 0.49% -1.57 0.0582 5.82%   -0.57 0.2843 28.43%   0.43 0.6664 66.64%   1.43 0.9236 92.36%   2.43 0.9925 99.25%
    -2.57 0.0051 0.51% -1.56 0.0594 5.94%   -0.56 0.2877 28.77%   0.44 0.6700 67.00%   1.44 0.9251 92.51%   2.44 0.9927 99.27%
    -2.56 0.0052 0.52% -1.55 0.0606 6.06%   -0.55 0.2912 29.12%   0.45 0.6736 67.36%   1.45 0.9265 92.65%   2.45 0.9929 99.29%
    -2.55 0.0054 0.54% -1.54 0.0618 6.18%   -0.54 0.2946 29.46%   0.46 0.6772 67.72%   1.46 0.9279 92.79%   2.46 0.9931 99.31%
    -2.54 0.0055 0.55% -1.53 0.0630 6.30%   -0.53 0.2981 29.81%   0.47 0.6808 68.08%   1.47 0.9292 92.92%   2.47 0.9932 99.32%
    -2.53 0.0057 0.57% -1.52 0.0643 6.43%   -0.52 0.3015 30.15%   0.48 0.6844 68.44%   1.48 0.9306 93.06%   2.48 0.9934 99.34%
    -2.52 0.0059 0.59% -1.51 0.0655 6.55%   -0.51 0.3150 31.50%   0.49 0.6879 68.79%   1.49 0.9319 93.19%   2.49 0.9936 99.36%
    -2.51 0.0060 0.60% -1.50 0.0668 6.68%   -0.50 0.3085 30.85%   0.50 0.6915 69.15%   1.50 0.9332 93.32%   2.50 0.9938 99.38%
    -2.50 0.0062 0.62% -1.49 0.0681 6.81%   -0.49 0.3121 31.21%   0.51 0.6950 69.50%   1.51 0.9345 93.45%   2.51 0.9940 99.40%
    -2.49 0.0064 0.64% -1.48 0.0694 6.94%   -0.48 0.3156 31.56%   0.52 0.6985 69.85%   1.52 0.9357 93.57%   2.52 0.9941 99.41%
    -2.48 0.0066 0.66% -1.47 0.0708 7.08%   -0.47 0.3192 31.92%   0.53 0.7019 70.19%   1.53 0.9370 93.70%   2.53 0.9943 99.43%
    -2.47 0.0068 0.68% -1.46 0.0722 7.22%   -0.46 0.3228 32.28%   0.54 0.7054 70.54%   1.54 0.9382 93.82%   2.54 0.9945 99.45%
    -2.46 0.0070 0.70% -1.45 0.0735 7.35%   -0.45 0.3264 32.64%   0.55 0.7088 70.88%   1.55 0.9394 93.94%   2.55 0.9946 99.46%
    -2.45 0.0071 0.71% -1.44 0.0749 7.49%   -0.44 0.3300 33.00%   0.56 0.7123 71.23%   1.56 0.9406 94.06%   2.56 0.9948 99.48%
    -2.44 0.0073 0.73% -1.43 0.0764 7.64%   -0.43 0.3336 33.36%   0.67 0.7157 71.57%   1.57 0.9418 94.18%   2.57 0.9949 99.49%
    -2.43 0.0076 0.76% -1.42 0.0778 7.78%   -0.42 0.3372 33.72%   0.58 0.7190 71.90%   1.58 0.9430 94.30%   2.58 0.9951 99.51%
    -2.42 0.0078 0.78% -1.41 0.0793 7.93%   -0.41 0.3409 34.09%   0.59 0.7224 72.24%   1.59 0.9441 94.41%   2.59 0.9952 99.52%
    -2.41 0.0080 0.80% -1.40 0.0808 8.08%   -0.40 0.3446 34.46%   0.60 0.7258 72.58%   1.60 0.9452 94.52%   2.60 0.9953 99.53%
    -2.40 0.0082 0.82% -1.39 0.0823 8.23%   -0.39 0.3483 34.83%   0.61 0.7291 72.91%   1.61 0.9463 94.63%   2.61 0.9955 99.55%
    -2.39 0.0084 0.84% -1.38 0.0838 8.38%   -0.38 0.3520 35.20%   0.62 0.7324 73.24%   1.62 0.9474 94.74%   2.62 0.9956 99.56%
    -2.38 0.0087 0.87% -1.37 0.0853 8.53%   -0.37 0.3557 35.57%   0.63 0.7357 73.57%   1.63 0.9485 94.85%   2.63 0.9957 99.57%
    -2.37 0.0089 0.89% -1.36 0.0869 8.69%   -0.36 0.3594 35.94%   0.64 0.7389 73.89%   1.64 0.9495 94.95%   2.64 0.9959 99.59%
    -2.36 0.0091 0.91% -1.35 0.0885 8.85%   -0.35 0.3632 36.32%   0.65 0.7422 74.22%   1.65 0.9505 95.05%   2.65 0.9960 99.60%
    -2.35 0.0094 0.94% -1.34 0.0901 9.01%   -0.34 0.3669 36.69%   0.66 0.7454 74.54%   1.66 0.9515 95.15%   2.66 0.9961 99.61%
    -2.34 0.0096 0.96% -1.33 0.0918 9.18%   -0.33 0.3707 37.07%   0.67 0.7486 74.86%   1.67 0.9525 95.25%   2.67 0.9962 99.62%
    -2.33 0.0099 0.99% -1.32 0.0934 9.34%   -0.32 0.3745 37.45%   0.68 0.7518 75.18%   1.68 0.9535 95.35%   2.68 0.9963 99.63%
    -2.32 0.0102 1.02% -1.31 0.0951 9.51%   -0.31 0.3783 37.83%   0.69 0.7549 75.49%   1.69 0.9545 95.45%   2.69 0.9964 99.64%
    -2.31 0.0104 1.04% -1.30 0.0968 9.68%   -0.30 0.3821 38.21%   0.70 0.7580 75.80%   1.70 0.9554 95.54%   2.70 0.9965 99.65%
    -2.30 0.0107 1.07% -1.29 0.0985 9.85%   -0.29 0.3859 38.59%   0.71 0.7612 76.12%   1.71 0.9564 95.64%   2.71 0.9968 99.68%
    -2.29 0.0110 1.10% -1.28 0.1003 10.03%   -0.28 0.3897 38.97%   0.72 0.7642 76.42%   1.72 0.9573 95.73%   2.72 0.9967 99.67%
    -2.28 0.0113 1.13% -1.27 0.1020 10.20%   -0.27 0.3936 39.36%   0.73 0.7673 76.73%   1.73 0.9582 95.82%   2.73 0.9968 99.68%
    -2.27 0.0116 1.16% -1.26 0.1038 10.38%   -0.26 0.3974 39.74%   0.74 0.7704 77.04%   1.74 0.9591 95.91%   2.74 0.9969 99.69%
    -2.26 0.0119 1.19% -1.25 0.1057 10.57%   -0.25 0.4013 40.13%   0.75 0.7734 77.34%   1.75 0.9599 95.99%   2.75 0.9970 99.70%
    -2.25 0.0122 1.22% -1.24 0.1075 10.75%   -0.24 0.4052 40.52%   0.76 0.7764 77.64%   1.76 0.9608 96.08%   2.76 0.9971 99.71%
    -2.24 0.0126 1.26% -1.23 0.1094 10.94%   -0.23 0.4091 40.91%   0.77 0.7794 77.94%   1.77 0.9616 96.16%   2.77 0.9972 99.72%
    -2.23 0.0129 1.29% -1.22 0.1112 11.12%   -0.22 0.4129 41.29%   0.78 0.7823 78.23%   1.78 0.9625 96.25%   2.78 0.9973 99.73%
    -2.22 0.0132 1.32% -1.21 0.1131 11.31%   -0.21 0.4168 41.68%   0.79 0.7852 78.52%   1.79 0.9633 96.33%   2.79 0.9974 99.74%
    -2.21 0.0136 1.36% -1.20 0.1151 11.51%   -0.20 0.4207 42.07%   0.80 0.7881 78.81%   1.80 0.9641 96.41%   2.80 0.9974 99.74%
    -2.20 0.0139 1.39% -1.19 0.1170 11.70%   -0.19 0.4247 42.47%   0.81 0.7910 79.10%   1.81 0.9649 96.49%   2.81 0.9975 99.75%
    -2.19 0.0143 1.43% -1.18 0.1190 11.90%   -0.18 0.4286 42.86%   0.82 0.7939 79.39%   1.82 0.9656 96.56%   2.82 0.9976 99.76%
    -2.18 0.0146 1.46% -1.17 0.1210 12.10%   -0.17 0.4325 43.25%   0.83 0.7967 79.67%   1.83 0.9664 96.64%   2.83 0.9977 99.77%
    -2.17 0.0150 1.50% -1.16 0.1230 12.30%   -0.16 0.4364 43.64%   0.84 0.7996 79.96%   1.84 0.9671 96.71%   2.84 0.9977 99.77%
    -2.16 0.0154 1.54% -1.15 0.1251 12.51%   -0.15 0.4404 44.04%   0.85 0.8023 80.23%   1.85 0.9678 96.78%   2.85 0.9978 99.78%
    -2.15 0.0158 1.58% -1.14 0.1271 12.71%   -0.14 0.4443 44.43%   0.86 0.8051 80.51%   1.86 0.9686 96.86%   2.86 0.9979 99.79%
    -2.14 0.0162 1.62% -1.13 0.1292 12.92%   -0.13 0.4483 44.83%   0.87 0.8079 80.79%   1.87 0.9693 96.93%   2.87 0.9980 99.80%
    -2.13 0.0166 1.66% -1.12 0.1314 13.14%   -0.12 0.4522 45.22%   0.88 0.8106 81.06%   1.88 0.9700 97.00%   2.88 0.9980 99.80%
    -2.12 0.0170 1.70% -1.11 0.1335 13.35%   -0.11 0.4562 45.62%   0.89 0.8133 81.33%   1.89 0.9706 97.06%   2.89 0.9981 99.81%
    -2.11 0.0174 1.74% -1.10 0.1357 13.57%   -0.10 0.4602 46.02%   0.90 0.8159 81.59%   1.90 0.9713 97.13%   2.90 0.9981 99.81%
    -2.10 0.0179 1.79% -1.09 0.1379 13.79%   -0.09 0.4641 46.41%   0.91 0.8186 81.86%   1.91 0.9719 97.19%   2.91 0.9982 99.82%
    -2.09 0.0183 1.83% -1.08 0.1401 14.01%   -0.08 0.4681 46.81%   0.92 0.8212 82.12%   1.92 0.9726 97.26%   2.92 0.9983 99.83%
    -2.08 0.0188 1.88% -1 07 0.1423 14.23%   -0.07 0.4721 47.21%   0.93 0.8238 82.38%   1.93 0.9732 97.32%   2.93 0.9983 99.83%
    -2.07 0.0192 1.92% -1.06 0.1446 14.46%   -0.06 0.4761 47.61%   0.94 0.8264 82.64%   1.94 0.9738 97.38%   2.94 0.9984 99.84%
    -2.06 0.0197 1.97% -1.05 0.1469 14.69%   -0.05 0.4801 48.01%   0.95 0.8289 82.89%   1.95 0.9744 97.44%   2.95 0.9984 99.84%
    -2.05 0.0202 2.02% -1.04 0.1492 14.92%   -0.04 0.4841 48.41%   0.96 0.8315 83.15%   1.96 0.9750 97.50%   2.96 0.9985 99.85%
    -2.04 0.0207 2.07% -1.03 0.1515 15.15%   -0.03 0.4880 48.80%   0.97 0.8340 83.40%   1.97 0.9756 97.56%   2.97 0.9985 99.85%
    -2.03 0.0212 2.12% -1.02 0.1539 15.39%   -0.02 0.4920 49.20%   0.98 0.8365 83.65%   1.98 0.9762 97.62%   2.98 0.9986 99.86%
    -2.02 0.0217 2.17% -1.01 0.1563 15.63%   -0.01 0.4960 49.60%   0.99 0.8389 83.89%   1.99 0.9767 97.67%   2.99 0.9986 99.86%
    -2.01 0.0222 2.22% -1.00 0.1587 15.87%   0.00 0.5000 50.00%   1.00 0.8413 84.13%   2.00 0.9773 97.73%   3.00 0.9987 99.87%
    -2.00 0.0228 2.28%                      
    Table 1\(\PageIndex{1}\): z Table. (CC-BY-SA; modified by Michelle Oja from Jsmura via Wikimedia Commons)

    Attributions & Contributors


    5.3.2: Table of Critical Values of z is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Michelle Oja.

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