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1.6.3.2: Table of Critical Values of z

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    22052
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    Table \(\PageIndex{1}\) shows negative z-scores, their probability (p-value), and percentage of scores that fall below that probability (p-value). Table \(\PageIndex{2}\) shows positive z-scores, their probability (p-value), and percentage of scores that fall below that probability (p-value) . 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 1\(\PageIndex{1}\): Negative z-Scores. (CC-BY-SA; modified by Michelle Oja from Jsmura via Wikimedia Commons)

     
    z-Score p-value % Below
    -3.00 0.0014 0.14%
    -2.99 0.0014 0.14%
    -2.98 0.0014 0.14%
    -2.97 0.0015 0.15%
    -2.96 0.0015 0.15%
    -2.95 0.0016 0.16%
    -2.94 0.0016 0.16%
    -2.93 0.0017 0.17%
    -2.92 0.0018 0.18%
    -2.91 0.0018 0.18%
    -2.90 0.0019 0.19%
    -2.89 0.0019 0.19%
    -2.88 0.0020 0.20%
    -2.87 0.0021 0.21%
    -2.86 0.0021 0.21%
    -2.85 0.0022 0.22%
    -2.84 0.0023 0.23%
    -2.83 0.0023 0.23%
    -2.82 0.0024 0.24%
    -2.81 0.0025 0.25%
    -2.80 0.0026 0.26%
    -2.79 0.0026 0.26%
    -2.78 0.0027 0.27%
    -2.77 0.0028 0.28%
    -2.76 0.0029 0.29%
    -2.75 0.0030 0.30%
    -2.74 0.0031 0.31%
    -2.73 0.0032 0.32%
    -2.72 0.0033 0.33%
    -2.71 0.0034 0.34%
    -2.70 0.0035 0.35%
    -2.69 0.0036 0.36%
    -2.68 0.0037 0.37%
    -2.67 0.0038 0.38%
    -2.66 0.0039 0.39%
    -2.65 0.0040 0.40%
    -2.64 0.0042 0.42%
    -2.63 0.0043 0.43%
    -2.62 0.0044 0.44%
    -2.61 0.0045 0.45%
    -2.60 0.0047 0.47%
    -2.59 0.0048 0.48%
    -2.58 0.0049 0.49%
    -2.57 0.0051 0.51%
    -2.56 0.0052 0.52%
    -2.55 0.0054 0.54%
    -2.54 0.0055 0.55%
    -2.53 0.0057 0.57%
    -2.52 0.0059 0.59%
    -2.51 0.0060 0.60%
    -2.50 0.0062 0.62%
    -2.49 0.0064 0.64%
    -2.48 0.0066 0.66%
    -2.47 0.0068 0.68%
    -2.46 0.0070 0.70%
    -2.45 0.0071 0.71%
    -2.44 0.0073 0.73%
    -2.43 0.0076 0.76%
    -2.42 0.0078 0.78%
    -2.41 0.0080 0.80%
    -2.40 0.0082 0.82%
    -2.39 0.0084 0.84%
    -2.38 0.0087 0.87%
    -2.37 0.0089 0.89%
    -2.36 0.0091 0.91%
    -2.35 0.0094 0.94%
    -2.34 0.0096 0.96%
    -2.33 0.0099 0.99%
    -2.32 0.0102 1.02%
    -2.31 0.0104 1.04%
    -2.30 0.0107 1.07%
    -2.29 0.0110 1.10%
    -2.28 0.0113 1.13%
    -2.27 0.0116 1.16%
    -2.26 0.0119 1.19%
    -2.25 0.0122 1.22%
    -2.24 0.0126 1.26%
    -2.23 0.0129 1.29%
    -2.22 0.0132 1.32%
    -2.21 0.0136 1.36%
    -2.20 0.0139 1.39%
    -2.19 0.0143 1.43%
    -2.18 0.0146 1.46%
    -2.17 0.0150 1.50%
    -2.16 0.0154 1.54%
    -2.15 0.0158 1.58%
    -2.14 0.0162 1.62%
    -2.13 0.0166 1.66%
    -2.12 0.0170 1.70%
    -2.11 0.0174 1.74%
    -2.10 0.0179 1.79%
    -2.09 0.0183 1.83%
    -2.08 0.0188 1.88%
    -2.07 0.0192 1.92%
    -2.06 0.0197 1.97%
    -2.05 0.0202 2.02%
    -2.04 0.0207 2.07%
    -2.03 0.0212 2.12%
    -2.02 0.0217 2.17%
    -2.01 0.0222 2.22%
    -2.00 0.0228 2.28%
    -1.99 0.0233 2.33%
    -1.98 0.0239 2.39%
    -1.97 0.0244 2.44%
    -1.96 0.0250 2.50%
    -1.95 0.0256 2.56%
    -1.94 0.0262 2.62%
    -1.93 0.0268 2.68%
    -1.92 0.0274 2.74%
    -1.91 0.0281 2.81%
    -1.90 0.0287 2.87%
    -1.89 0.0294 2.94%
    -1.88 0.0301 3.01%
    -1.87 0.0307 3.07%
    -1.86 0.0314 3.14%
    -1.85 0.0322 3.22%
    -1.84 0.0329 3.29%
    -1.83 0.0336 3.36%
    -1.82 0.0344 3.44%
    -1.81 0.0352 3.52%
    -1.80 0.0359 3.59%
    -1.79 0.0367 3.67%
    -1.78 0.0375 3.75%
    -1.77 0.0384 3.84%
    -1.76 0.0392 3.92%
    -1.75 0.0401 4.01%
    -1.74 0.0409 4.09%
    -1.73 0.0418 4.18%
    -1.72 0.0427 4.27%
    -1.71 0.0436 4.36%
    -1.70 0.0446 4.46%
    -1.69 0.0455 4.55%
    -1.68 0.0465 4.65%
    -1.67 0.0475 4.75%
    -1.66 0.0485 4.85%
    -1.65 0.0495 4.95%
    -1.64 0.0505 5.05%
    -1.63 0.0516 5.16%
    -1.62 0.0526 5.26%
    -1.61 0.0537 5.37%
    -1.60 0.0548 5.48%
    -1.59 0.0559 5.59%
    -1.58 0.0571 5.71%
    -1.57 0.0582 5.82%
    -1.56 0.0594 5.94%
    -1.55 0.0606 6.06%
    -1.54 0.0618 6.18%
    -1.53 0.0630 6.30%
    -1.52 0.0643 6.43%
    -1.51 0.0655 6.55%
    -1.50 0.0668 6.68%
    -1.49 0.0681 6.81%
    -1.48 0.0694 6.94%
    -1.47 0.0708 7.08%
    -1.46 0.0722 7.22%
    -1.45 0.0735 7.35%
    -1.44 0.0749 7.49%
    -1.43 0.0764 7.64%
    -1.42 0.0778 7.78%
    -1.41 0.0793 7.93%
    -1.40 0.0808 8.08%
    -1.39 0.0823 8.23%
    -1.38 0.0838 8.38%
    -1.37 0.0853 8.53%
    -1.36 0.0869 8.69%
    -1.35 0.0885 8.85%
    -1.34 0.0901 9.01%
    -1.33 0.0918 9.18%
    -1.32 0.0934 9.34%
    -1.31 0.0951 9.51%
    -1.30 0.0968 9.68%
    -1.29 0.0985 9.85%
    -1.28 0.1003 10.03%
    -1.27 0.1020 10.20%
    -1.26 0.1038 10.38%
    -1.25 0.1057 10.57%
    -1.24 0.1075 10.75%
    -1.23 0.1094 10.94%
    -1.22 0.1112 11.12%
    -1.21 0.1131 11.31%
    -1.20 0.1151 11.51%
    -1.19 0.1170 11.70%
    -1.18 0.1190 11.90%
    -1.17 0.1210 12.10%
    -1.16 0.1230 12.30%
    -1.15 0.1251 12.51%
    -1.14 0.1271 12.71%
    -1.13 0.1292 12.92%
    -1.12 0.1314 13.14%
    -1.11 0.1335 13.35%
    -1.10 0.1357 13.57%
    -1.09 0.1379 13.79%
    -1.08 0.1401 14.01%
    -1 07 0.1423 14.23%
    -1.06 0.1446 14.46%
    -1.05 0.1469 14.69%
    -1.04 0.1492 14.92%
    -1.03 0.1515 15.15%
    -1.02 0.1539 15.39%
    -1.01 0.1563 15.63%
    -1.00 0.1587 15.87%
    -0.99 0.1611 16.11%
    -0 98 0.1635 16.35%
    -0.97 0.1660 16.60%
    -0.96 0.1685 16.85%
    -0.95 0.1711 17.11%
    -0.94 0.1736 17.36%
    -0.93 0.1762 17.62%
    -0.92 0.1788 17.88%
    -0.91 0.1814 18.14%
    -0.90 0.1841 18.41%
    -0.89 0.1867 18.67%
    -0.88 0.1894 18.94%
    -0.87 0.1922 19.22%
    -0.86 0.1949 19.49%
    -0.85 0.1977 19.77%
    -0.84 0.2005 20.05%
    -0.83 0.2033 20.33%
    -0.82 0.2061 20.61%
    -0.81 0.2090 20.90%
    -0.80 0.2119 21.19%
    -0.79 0.2148 21.48%
    -0.78 0.2177 21.77%
    -0.77 0.2207 22.07%
    -0.76 0.2236 22.36%
    -0.75 0.2266 22.66%
    -0.74 0.2297 22.97%
    -0.73 0.2327 23.27%
    -0.72 0.2358 23.58%
    -0.71 0.2389 23.89%
    -0.70 0.2420 24.20%
    -0.69 0.2451 24.51%
    -0.68 0.2483 24.83%
    -0.67 0.2514 25.14%
    -0.66 0.2546 25.46%
    -0.65 0.2579 25.79%
    -0.64 0.2611 26.11%
    -0.63 0.2644 26.44%
    -0.62 0.2676 26.76%
    -0.61 0.2709 27.09%
    -0.60 0.2743 27.43%
    -0.59 0.2776 27.76%
    -0.58 0.2810 28.10%
    -0.57 0.2843 28.43%
    -0.56 0.2877 28.77%
    -0.55 0.2912 29.12%
    -0.54 0.2946 29.46%
    -0.53 0.2981 29.81%
    -0.52 0.3015 30.15%
    -0.51 0.3150 31.50%
    -0.50 0.3085 30.85%
    -0.49 0.3121 31.21%
    -0.48 0.3156 31.56%
    -0.47 0.3192 31.92%
    -0.46 0.3228 32.28%
    -0.45 0.3264 32.64%
    -0.44 0.3300 33.00%
    -0.43 0.3336 33.36%
    -0.42 0.3372 33.72%
    -0.41 0.3409 34.09%
    -0.40 0.3446 34.46%
    -0.39 0.3483 34.83%
    -0.38 0.3520 35.20%
    -0.37 0.3557 35.57%
    -0.36 0.3594 35.94%
    -0.35 0.3632 36.32%
    -0.34 0.3669 36.69%
    -0.33 0.3707 37.07%
    -0.32 0.3745 37.45%
    -0.31 0.3783 37.83%
    -0.30 0.3821 38.21%
    -0.29 0.3859 38.59%
    -0.28 0.3897 38.97%
    -0.27 0.3936 39.36%
    -0.26 0.3974 39.74%
    -0.25 0.4013 40.13%
    -0.24 0.4052 40.52%
    -0.23 0.4091 40.91%
    -0.22 0.4129 41.29%
    -0.21 0.4168 41.68%
    -0.20 0.4207 42.07%
    -0.19 0.4247 42.47%
    -0.18 0.4286 42.86%
    -0.17 0.4325 43.25%
    -0.16 0.4364 43.64%
    -0.15 0.4404 44.04%
    -0.14 0.4443 44.43%
    -0.13 0.4483 44.83%
    -0.12 0.4522 45.22%
    -0.11 0.4562 45.62%
    -0.10 0.4602 46.02%
    -0.09 0.4641 46.41%
    -0.08 0.4681 46.81%
    -0.07 0.4721 47.21%
    -0.06 0.4761 47.61%
    -0.05 0.4801 48.01%
    -0.04 0.4841 48.41%
    -0.03 0.4880 48.80%
    -0.02 0.4920 49.20%
    -0.01 0.4960 49.60%

    Table 2\(\PageIndex{2}\): Positive z-Scores. (CC-BY-SA; modified by Michelle Oja from Jsmura via Wikimedia Commons)

    Positive z-score
    z-Score p-value % Below
    0.00 0.5000 50.00%
    0.01 0.5040 50.40%
    0.02 0.5080 50.80%
    0.03 0.5120 51.20%
    0.04 0.5160 51.60%
    0.05 0.5199 51.99%
    0.06 0.5239 52.39%
    0.07 0.5279 52.79%
    0.08 0.5319 53.19%
    0.09 0.5359 53.59%
    0.10 0.5398 53.98%
    0.11 0.5438 54.38%
    0.12 0.5478 54.78%
    0.13 0.5517 55.17%
    0.14 0.5557 55.57%
    0.15 0.5596 55.96%
    0.16 0.5636 56.36%
    0.17 0.5675 56.75%
    0.18 0.5714 57.14%
    0.19 0.5754 57.54%
    0.20 0.5793 57.93%
    0.21 0.5832 58.32%
    0.22 0.5871 58.71%
    0.23 0.5910 59.10%
    0.24 0.5948 59.48%
    0.25 0.5987 59.87%
    0.26 0.6026 60.26%
    0.27 0.6064 60.64%
    0.28 0.6103 61.03%
    0.29 0.6141 61.41%
    0.30 0.6179 61.79%
    0.31 0.6217 62.17%
    0.32 0.6255 62.55%
    0.33 0.6293 62.93%
    0.34 0.6331 63.31%
    0.35 0.6368 63.68%
    0.36 0.6406 64.06%
    0.37 0.6443 64.43%
    0.38 0.6480 64.80%
    0.39 0.6517 65.17%
    0.40 0.6554 65.54%
    0.41 0.6591 65.91%
    0.42 0.6628 66.28%
    0.43 0.6664 66.64%
    0.44 0.6700 67.00%
    0.45 0.6736 67.36%
    0.46 0.6772 67.72%
    0.47 0.6808 68.08%
    0.48 0.6844 68.44%
    0.49 0.6879 68.79%
    0.50 0.6915 69.15%
    0.51 0.6950 69.50%
    0.52 0.6985 69.85%
    0.53 0.7019 70.19%
    0.54 0.7054 70.54%
    0.55 0.7088 70.88%
    0.56 0.7123 71.23%
    0.67 0.7157 71.57%
    0.58 0.7190 71.90%
    0.59 0.7224 72.24%
    0.60 0.7258 72.58%
    0.61 0.7291 72.91%
    0.62 0.7324 73.24%
    0.63 0.7357 73.57%
    0.64 0.7389 73.89%
    0.65 0.7422 74.22%
    0.66 0.7454 74.54%
    0.67 0.7486 74.86%
    0.68 0.7518 75.18%
    0.69 0.7549 75.49%
    0.70 0.7580 75.80%
    0.71 0.7612 76.12%
    0.72 0.7642 76.42%
    0.73 0.7673 76.73%
    0.74 0.7704 77.04%
    0.75 0.7734 77.34%
    0.76 0.7764 77.64%
    0.77 0.7794 77.94%
    0.78 0.7823 78.23%
    0.79 0.7852 78.52%
    0.80 0.7881 78.81%
    0.81 0.7910 79.10%
    0.82 0.7939 79.39%
    0.83 0.7967 79.67%
    0.84 0.7996 79.96%
    0.85 0.8023 80.23%
    0.86 0.8051 80.51%
    0.87 0.8079 80.79%
    0.88 0.8106 81.06%
    0.89 0.8133 81.33%
    0.90 0.8159 81.59%
    0.91 0.8186 81.86%
    0.92 0.8212 82.12%
    0.93 0.8238 82.38%
    0.94 0.8264 82.64%
    0.95 0.8289 82.89%
    0.96 0.8315 83.15%
    0.97 0.8340 83.40%
    0.98 0.8365 83.65%
    0.99 0.8389 83.89%
    1.00 0.8413 84.13%
    1.01 0.8438 84.38%
    1.02 0.8461 84.61%
    1.03 0.8485 84.85%
    1.04 0.8508 85.08%
    1.05 0.8531 85.31%
    1.06 0.8554 85.54%
    1.07 0.8577 85.77%
    1.08 0.8599 85.99%
    1.09 0.8621 86.21%
    1.10 0.8643 86.43%
    1.11 0.8665 86.65%
    1.12 0.8686 86.86%
    1.13 0.8708 87.08%
    1.14 0.8729 87.29%
    1.15 0.8749 87.49%
    1.16 0.8770 87.70%
    1.17 0.8790 87.90%
    1.18 0.8810 88.10%
    1.19 0.8830 88.30%
    1.20 0.8849 88.49%
    1.21 0.8869 88.69%
    1.22 0.8838 88.38%
    1.23 0.8907 89.07%
    1.24 0.8925 89.25%
    1.25 0.8944 89.44%
    1.26 0.8562 85.62%
    1.27 0.8980 89.80%
    1.28 0.8997 89.97%
    1.29 0.9015 90.15%
    1.30 0.9032 90.32%
    1.31 0.9349 93.49%
    1.32 0.9366 93.66%
    1.33 0.9382 93.82%
    1.34 0.9099 90.99%
    1.35 0.9115 91.15%
    1.36 0.9131 91.31%
    1.37 0.9147 91.47%
    1.38 0.9162 91.62%
    1.39 0.9177 91.77%
    1.40 0.9192 91.92%
    1.41 0.9207 92.07%
    1.42 0.9222 92.22%
    1.43 0.9236 92.36%
    1.44 0.9251 92.51%
    1.45 0.9265 92.65%
    1.46 0.9279 92.79%
    1.47 0.9292 92.92%
    1.48 0.9306 93.06%
    1.49 0.9319 93.19%
    1.50 0.9332 93.32%
    1.51 0.9345 93.45%
    1.52 0.9357 93.57%
    1.53 0.9370 93.70%
    1.54 0.9382 93.82%
    1.55 0.9394 93.94%
    1.56 0.9406 94.06%
    1.57 0.9418 94.18%
    1.58 0.9430 94.30%
    1.59 0.9441 94.41%
    1.60 0.9452 94.52%
    1.61 0.9463 94.63%
    1.62 0.9474 94.74%
    1.63 0.9485 94.85%
    1.64 0.9495 94.95%
    1.65 0.9505 95.05%
    1.66 0.9515 95.15%
    1.67 0.9525 95.25%
    1.68 0.9535 95.35%
    1.69 0.9545 95.45%
    1.70 0.9554 95.54%
    1.71 0.9564 95.64%
    1.72 0.9573 95.73%
    1.73 0.9582 95.82%
    1.74 0.9591 95.91%
    1.75 0.9599 95.99%
    1.76 0.9608 96.08%
    1.77 0.9616 96.16%
    1.78 0.9625 96.25%
    1.79 0.9633 96.33%
    1.80 0.9641 96.41%
    1.81 0.9649 96.49%
    1.82 0.9656 96.56%
    1.83 0.9664 96.64%
    1.84 0.9671 96.71%
    1.85 0.9678 96.78%
    1.86 0.9686 96.86%
    1.87 0.9693 96.93%
    1.88 0.9700 97.00%
    1.89 0.9706 97.06%
    1.90 0.9713 97.13%
    1.91 0.9719 97.19%
    1.92 0.9726 97.26%
    1.93 0.9732 97.32%
    1.94 0.9738 97.38%
    1.95 0.9744 97.44%
    1.96 0.9750 97.50%
    1.97 0.9756 97.56%
    1.98 0.9762 97.62%
    1.99 0.9767 97.67%
    2.00 0.9773 97.73%
    2.01 0.9778 97.78%
    2.02 0.9783 97.83%
    2.03 0.9788 97.88%
    2.04 0.9793 97.93%
    2.05 0.9798 97.98%
    2.06 0.9803 98.03%
    2.07 0.9808 98.08%
    2.08 0.9812 98.12%
    2.09 0.9817 98.17%
    2.10 0.9821 98.21%
    2.11 0.9826 98.26%
    2.12 0.9830 98.30%
    2.13 0.9834 98.34%
    2.14 0.9838 98.38%
    2.15 0.9842 98.42%
    2.16 0.9846 98.46%
    2.17 0.9850 98.50%
    2.18 0.9854 98.54%
    2.19 0.9857 98.57%
    2.20 0.9861 98.61%
    2.21 0.9865 98.65%
    2.22 0.9868 98.68%
    2.23 0.9871 98.71%
    2.24 0.9875 98.75%
    2.25 0.9878 98.78%
    2.26 0.9881 98.81%
    2.27 0.9884 98.84%
    2.28 0.9887 98.87%
    2.29 0.9890 98.90%
    2.30 0.9893 98.93%
    2.31 0.9896 98.96%
    2.32 0.9898 98.98%
    2.33 0.9901 99.01%
    2.34 0.9904 99.04%
    2.35 0.9906 99.06%
    2.36 0.9909 99.09%
    2.37 0.9911 99.11%
    2.38 0.9913 99.13%
    2.39 0.9916 99.16%
    2.40 0.9918 99.18%
    2.41 0.9920 99.20%
    2.42 0.9922 99.22%
    2.43 0.9925 99.25%
    2.44 0.9927 99.27%
    2.45 0.9929 99.29%
    2.46 0.9931 99.31%
    2.47 0.9932 99.32%
    2.48 0.9934 99.34%
    2.49 0.9936 99.36%
    2.50 0.9938 99.38%
    2.51 0.9940 99.40%
    2.52 0.9941 99.41%
    2.53 0.9943 99.43%
    2.54 0.9945 99.45%
    2.55 0.9946 99.46%
    2.56 0.9948 99.48%
    2.57 0.9949 99.49%
    2.58 0.9951 99.51%
    2.59 0.9952 99.52%
    2.60 0.9953 99.53%
    2.61 0.9955 99.55%
    2.62 0.9956 99.56%
    2.63 0.9957 99.57%
    2.64 0.9959 99.59%
    2.65 0.9960 99.60%
    2.66 0.9961 99.61%
    2.67 0.9962 99.62%
    2.68 0.9963 99.63%
    2.69 0.9964 99.64%
    2.70 0.9965 99.65%
    2.71 0.9968 99.68%
    2.72 0.9967 99.67%
    2.73 0.9968 99.68%
    2.74 0.9969 99.69%
    2.75 0.9970 99.70%
    2.76 0.9971 99.71%
    2.77 0.9972 99.72%
    2.78 0.9973 99.73%
    2.79 0.9974 99.74%
    2.80 0.9974 99.74%
    2.81 0.9975 99.75%
    2.82 0.9976 99.76%
    2.83 0.9977 99.77%
    2.84 0.9977 99.77%
    2.85 0.9978 99.78%
    2.86 0.9979 99.79%
    2.87 0.9980 99.80%
    2.88 0.9980 99.80%
    2.89 0.9981 99.81%
    2.90 0.9981 99.81%
    2.91 0.9982 99.82%
    2.92 0.9983 99.83%
    2.93 0.9983 99.83%
    2.94 0.9984 99.84%
    2.95 0.9984 99.84%
    2.96 0.9985 99.85%
    2.97 0.9985 99.85%
    2.98 0.9986 99.86%
    2.99 0.9986 99.86%
    3.00 0.9987 99.87%

    Attributions & Contributors


    This page titled 1.6.3.2: 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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