16.1: Standard Normal Distribution Table (z table)
- Page ID
- 55357
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The image below is labeled with A, B, C, and D, which correspond to columns in the table.
- A refers to the \(z\) score.
- B refers to the body, the larger area on one side of a \(z\)-score.
- C refers to the tail, the smaller area on one side of a \(z\)-score.
- D refers to the area between the mean and the \(z\)-score.
This table provides only positive \(z\)-scores, as the standard normal distribution is symmetric.
| (A) \(z\) | (B) Proportion in Body | (C) Proportion in Tail | (D) Proportion between Mean and \(z\) |
|---|---|---|---|
| 0.00 | .5000 | .5000 | .0000 |
| 0.01 | .5040 | .4960 | .0040 |
| 0.02 | .5080 | .4920 | .0080 |
| 0.03 | .5120 | .4880 | .0120 |
| 0.04 | .5160 | .4840 | .0160 |
| 0.05 | .5199 | .4801 | .0199 |
| 0.06 | .5239 | .4761 | .0239 |
| 0.07 | .5279 | .4721 | .0279 |
| 0.08 | .5319 | .4681 | .0319 |
| 0.09 | .5359 | .4641 | .0359 |
| 0.10 | .5398 | .4602 | .0398 |
| 0.11 | .5438 | .4562 | .0438 |
| 0.12 | .5478 | .4522 | .0478 |
| 0.13 | .5517 | .4483 | .0517 |
| 0.14 | .5557 | .4443 | .0557 |
| 0.15 | .5596 | .4404 | .0596 |
| 0.16 | .5636 | .4364 | .0636 |
| 0.17 | .5675 | .4325 | .0675 |
| 0.18 | .5714 | .4286 | .0714 |
| 0.19 | .5753 | .4247 | .0753 |
| 0.20 | .5793 | .4207 | .0793 |
| 0.21 | .5832 | .4168 | .0832 |
| 0.22 | .5871 | .4129 | .0871 |
| 0.23 | .5910 | .4090 | .0910 |
| 0.24 | .5948 | .4052 | .0948 |
| 0.25 | .5987 | .4013 | .0987 |
| 0.26 | .6026 | .3974 | .1026 |
| 0.27 | .6064 | .3936 | .1064 |
| 0.28 | .6103 | .3897 | .1103 |
| 0.29 | .6141 | .3859 | .1141 |
| 0.30 | .6179 | .3821 | .1179 |
| 0.31 | .6217 | .3783 | .1217 |
| 0.32 | .6255 | .3745 | .1255 |
| 0.33 | .6293 | .3707 | .1293 |
| 0.34 | .6331 | .3669 | .1331 |
| 0.35 | .6368 | .3632 | .1368 |
| 0.36 | .6406 | .3594 | .1406 |
| 0.37 | .6443 | .3557 | .1443 |
| 0.38 | .6480 | .3520 | .1480 |
| 0.39 | .6517 | .3483 | .1517 |
| 0.40 | .6554 | .3446 | .1554 |
| 0.41 | .6591 | .3409 | .1591 |
| 0.42 | .6628 | .3372 | .1628 |
| 0.43 | .6664 | .3336 | .1664 |
| 0.44 | .6700 | .3300 | .1700 |
| 0.45 | .6736 | .3264 | .1736 |
| 0.46 | .6772 | .3228 | .1772 |
| 0.47 | .6808 | .3192 | .1808 |
| 0.48 | .6844 | .3156 | .1844 |
| 0.49 | .6879 | .3121 | .1879 |
| 0.50 | .6915 | .3085 | .1915 |
| 0.51 | .6950 | .3050 | .1950 |
| 0.52 | .6985 | .3015 | .1985 |
| 0.53 | .7019 | .2981 | .2019 |
| 0.54 | .7054 | .2946 | .2054 |
| 0.55 | .7088 | .2912 | .2088 |
| 0.56 | .7123 | .2877 | .2123 |
| 0.57 | .7157 | .2843 | .2157 |
| 0.58 | .7190 | .2810 | .2190 |
| 0.59 | .7224 | .2776 | .2224 |
| 0.60 | .7257 | .2743 | .2257 |
| 0.61 | .7291 | .2709 | .2291 |
| 0.62 | .7324 | .2676 | .2324 |
| 0.63 | .7357 | .2643 | .2357 |
| 0.64 | .7389 | .2611 | .2389 |
| 0.65 | .7422 | .2578 | .2422 |
| 0.66 | .7454 | .2546 | .2454 |
| 0.67 | .7486 | .2514 | .2486 |
| 0.68 | .7517 | .2483 | .2517 |
| 0.69 | .7549 | .2451 | .2549 |
| 0.70 | .7580 | .2420 | .2580 |
| 0.71 | .7611 | .2389 | .2611 |
| 0.72 | .7642 | .2358 | .2642 |
| 0.73 | .7673 | .2327 | .2673 |
| 0.74 | .7704 | .2296 | .2704 |
| 0.75 | .7734 | .2266 | .2734 |
| 0.76 | .7764 | .2236 | .2764 |
| 0.77 | .7794 | .2206 | .2794 |
| 0.78 | .7823 | .2177 | .2823 |
| 0.79 | .7852 | .2148 | .2852 |
| 0.80 | .7881 | .2119 | .2881 |
| 0.81 | .7910 | .2090 | .2910 |
| 0.82 | .7939 | .2061 | .2939 |
| 0.83 | .7967 | .2033 | .2967 |
| 0.84 | .7995 | .2005 | .2995 |
| 0.85 | .8023 | .1977 | .3023 |
| 0.86 | .8051 | .1949 | .3051 |
| 0.87 | .8078 | .1922 | .3078 |
| 0.88 | .8106 | .1894 | .3106 |
| 0.89 | .8133 | .1867 | .3133 |
| 0.90 | .8159 | .1841 | .3159 |
| 0.91 | .8186 | .1814 | .3186 |
| 0.92 | .8212 | .1788 | .3212 |
| 0.93 | .8238 | .1762 | .3238 |
| 0.94 | .8264 | .1736 | .3264 |
| 0.95 | .8289 | .1711 | .3289 |
| 0.96 | .8315 | .1685 | .3315 |
| 0.97 | .8340 | .1660 | .3340 |
| 0.98 | .8365 | .1635 | .3365 |
| 0.99 | .8389 | .1611 | .3389 |
| 1.00 | .8413 | .1587 | .3413 |
| 1.01 | .8438 | .1562 | .3438 |
| 1.02 | .8461 | .1539 | .3461 |
| 1.03 | .8485 | .1515 | .3485 |
| 1.04 | .8508 | .1492 | .3508 |
| 1.05 | .8531 | .1469 | .3531 |
| 1.06 | .8554 | .1446 | .3554 |
| 1.07 | .8577 | .1423 | .3577 |
| 1.08 | .8599 | .1401 | .3599 |
| 1.09 | .8621 | .1379 | .3621 |
| 1.10 | .8643 | .1357 | .3643 |
| 1.11 | .8665 | .1335 | .3665 |
| 1.12 | .8686 | .1314 | .3686 |
| 1.13 | .8708 | .1292 | .3708 |
| 1.14 | .8729 | .1271 | .3729 |
| 1.15 | .8749 | .1251 | .3749 |
| 1.16 | .8770 | .1230 | .3770 |
| 1.17 | .8790 | .1210 | .3790 |
| 1.18 | .8810 | .1190 | .3810 |
| 1.19 | .8830 | .1170 | .3830 |
| 1.20 | .8849 | .1151 | .3849 |
| 1.21 | .8869 | .1131 | .3869 |
| 1.22 | .8888 | .1112 | .3888 |
| 1.23 | .8907 | .1093 | .3907 |
| 1.24 | .8925 | .1075 | .3925 |
| 1.25 | .8944 | .1056 | .3944 |
| 1.26 | .8962 | .1038 | .3962 |
| 1.27 | .8980 | .1020 | .3980 |
| 1.28 | .8997 | .1003 | .3997 |
| 1.29 | .9015 | .0985 | .4015 |
| 1.30 | .9032 | .0968 | .4032 |
| 1.31 | .9049 | .0951 | .4049 |
| 1.32 | .9066 | .0934 | .4066 |
| 1.33 | .9082 | .0918 | .4082 |
| 1.34 | .9099 | .0901 | .4099 |
| 1.35 | .9115 | .0885 | .4115 |
| 1.36 | .9131 | .0869 | .4131 |
| 1.37 | .9147 | .0853 | .4147 |
| 1.38 | .9162 | .0838 | .4162 |
| 1.39 | .9177 | .0823 | .4177 |
| 1.40 | .9192 | .0808 | .4192 |
| 1.41 | .9207 | .0793 | .4207 |
| 1.42 | .9222 | .0778 | .4222 |
| 1.43 | .9236 | .0764 | .4236 |
| 1.44 | .9251 | .0749 | .4251 |
| 1.45 | .9265 | .0735 | .4265 |
| 1.46 | .9279 | .0721 | .4279 |
| 1.47 | .9292 | .0708 | .4292 |
| 1.48 | .9306 | .0694 | .4306 |
| 1.49 | .9319 | .0681 | .4319 |
| 1.50 | .9332 | .0668 | .4332 |
| 1.51 | .9345 | .0655 | .4345 |
| 1.52 | .9357 | .0643 | .4357 |
| 1.53 | .9370 | .0630 | .4370 |
| 1.54 | .9382 | .0618 | .4382 |
| 1.55 | .9394 | .0606 | .4394 |
| 1.56 | .9406 | .0594 | .4406 |
| 1.57 | .9418 | .0582 | .4418 |
| 1.58 | .9429 | .0571 | .4429 |
| 1.59 | .9441 | .0559 | .4441 |
| 1.60 | .9452 | .0548 | .4452 |
| 1.61 | .9463 | .0537 | .4463 |
| 1.62 | .9474 | .0526 | .4474 |
| 1.63 | .9484 | .0516 | .4484 |
| 1.64 | .9495 | .0505 | .4495 |
| 1.65 | .9505 | .0495 | .4505 |
| 1.66 | .9515 | .0485 | .4515 |
| 1.67 | .9525 | .0475 | .4525 |
| 1.68 | .9535 | .0465 | .4535 |
| 1.69 | .9545 | .0455 | .4545 |
| 1.70 | .9554 | .0446 | .4554 |
| 1.71 | .9564 | .0436 | .4564 |
| 1.72 | .9573 | .0427 | .4573 |
| 1.73 | .9582 | .0418 | .4582 |
| 1.74 | .9591 | .0409 | .4591 |
| 1.75 | .9599 | .0401 | .4599 |
| 1.76 | .9608 | .0392 | .4608 |
| 1.77 | .9616 | .0384 | .4616 |
| 1.78 | .9625 | .0375 | .4625 |
| 1.79 | .9633 | .0367 | .4633 |
| 1.80 | .9641 | .0359 | .4641 |
| 1.81 | .9649 | .0351 | .4649 |
| 1.82 | .9656 | .0344 | .4656 |
| 1.83 | .9664 | .0336 | .4664 |
| 1.84 | .9671 | .0329 | .4671 |
| 1.85 | .9678 | .0322 | .4678 |
| 1.86 | .9686 | .0314 | .4686 |
| 1.87 | .9693 | .0307 | .4693 |
| 1.88 | .9699 | .0301 | .4699 |
| 1.89 | .9706 | .0294 | .4706 |
| 1.90 | .9713 | .0287 | .4713 |
| 1.91 | .9719 | .0281 | .4719 |
| 1.92 | .9726 | .0274 | .4726 |
| 1.93 | .9732 | .0268 | .4732 |
| 1.94 | .9738 | .0262 | .4738 |
| 1.95 | .9744 | .0256 | .4744 |
| 1.96 | .9750 | .0250 | .4750 |
| 1.97 | .9756 | .0244 | .4756 |
| 1.98 | .9761 | .0239 | .4761 |
| 1.99 | .9767 | .0233 | .4767 |
| 2.00 | .9772 | .0228 | .4772 |
| 2.01 | .9778 | .0222 | .4778 |
| 2.02 | .9783 | .0217 | .4783 |
| 2.03 | .9788 | .0212 | .4788 |
| 2.04 | .9793 | .0207 | .4793 |
| 2.05 | .9798 | .0202 | .4798 |
| 2.06 | .9803 | .0197 | .4803 |
| 2.07 | .9808 | .0192 | .4808 |
| 2.08 | .9812 | .0188 | .4812 |
| 2.09 | .9817 | .0183 | .4817 |
| 2.10 | .9821 | .0179 | .4821 |
| 2.11 | .9826 | .0174 | .4826 |
| 2.12 | .9830 | .0170 | .4830 |
| 2.13 | .9834 | .0166 | .4834 |
| 2.14 | .9838 | .0162 | .4838 |
| 2.15 | .9842 | .0158 | .4842 |
| 2.16 | .9846 | .0154 | .4846 |
| 2.17 | .9850 | .0150 | .4850 |
| 2.18 | .9854 | .0146 | .4854 |
| 2.19 | .9857 | .0143 | .4857 |
| 2.20 | .9861 | .0139 | .4861 |
| 2.21 | .9864 | .0136 | .4864 |
| 2.22 | .9868 | .0132 | .4868 |
| 2.23 | .9871 | .0129 | .4871 |
| 2.24 | .9875 | .0125 | .4875 |
| 2.25 | .9878 | .0122 | .4878 |
| 2.26 | .9881 | .0119 | .4881 |
| 2.27 | .9884 | .0116 | .4884 |
| 2.28 | .9887 | .0113 | .4887 |
| 2.29 | .9890 | .0110 | .4890 |
| 2.30 | .9893 | .0107 | .4893 |
| 2.31 | .9896 | .0104 | .4896 |
| 2.32 | .9898 | .0102 | .4898 |
| 2.33 | .9901 | .0099 | .4901 |
| 2.34 | .9904 | .0096 | .4904 |
| 2.35 | .9906 | .0094 | .4906 |
| 2.36 | .9909 | .0091 | .4909 |
| 2.37 | .9911 | .0089 | .4911 |
| 2.38 | .9913 | .0087 | .4913 |
| 2.39 | .9916 | .0084 | .4916 |
| 2.40 | .9918 | .0082 | .4918 |
| 2.41 | .9920 | .0080 | .4920 |
| 2.42 | .9922 | .0078 | .4922 |
| 2.43 | .9925 | .0075 | .4925 |
| 2.44 | .9927 | .0073 | .4927 |
| 2.45 | .9929 | .0071 | .4929 |
| 2.46 | .9931 | .0069 | .4931 |
| 2.47 | .9932 | .0068 | .4932 |
| 2.48 | .9934 | .0066 | .4934 |
| 2.49 | .9936 | .0064 | .4936 |
| 2.50 | .9938 | .0062 | .4938 |
| 2.51 | .9940 | .0060 | .4940 |
| 2.52 | .9941 | .0059 | .4941 |
| 2.53 | .9943 | .0057 | .4943 |
| 2.54 | .9945 | .0055 | .4945 |
| 2.55 | .9946 | .0054 | .4946 |
| 2.56 | .9948 | .0052 | .4948 |
| 2.57 | .9949 | .0051 | .4949 |
| 2.58 | .9951 | .0049 | .4951 |
| 2.59 | .9952 | .0048 | .4952 |
| 2.60 | .9953 | .0047 | .4953 |
| 2.61 | .9955 | .0045 | .4955 |
| 2.62 | .9956 | .0044 | .4956 |
| 2.63 | .9957 | .0043 | .4957 |
| 2.64 | .9959 | .0041 | .4959 |
| 2.65 | .9960 | .0040 | .4960 |
| 2.66 | .9961 | .0039 | .4961 |
| 2.67 | .9962 | .0038 | .4962 |
| 2.68 | .9963 | .0037 | .4963 |
| 2.69 | .9964 | .0036 | .4964 |
| 2.70 | .9965 | .0035 | .4965 |
| 2.71 | .9966 | .0034 | .4966 |
| 2.72 | .9967 | .0033 | .4967 |
| 2.73 | .9968 | .0032 | .4968 |
| 2.74 | .9969 | .0031 | .4969 |
| 2.75 | .9970 | .0030 | .4970 |
| 2.76 | .9971 | .0029 | .4971 |
| 2.77 | .9972 | .0028 | .4972 |
| 2.78 | .9973 | .0027 | .4973 |
| 2.79 | .9974 | .0026 | .4974 |
| 2.80 | .9974 | .0026 | .4974 |
| 2.81 | .9975 | .0025 | .4975 |
| 2.82 | .9976 | .0024 | .4976 |
| 2.83 | .9977 | .0023 | .4977 |
| 2.84 | .9977 | .0023 | .4977 |
| 2.85 | .9978 | .0022 | .4978 |
| 2.86 | .9979 | .0021 | .4979 |
| 2.87 | .9979 | .0021 | .4979 |
| 2.88 | .9980 | .0020 | .4980 |
| 2.89 | .9981 | .0019 | .4981 |
| 2.90 | .9981 | .0019 | .4981 |
| 2.91 | .9982 | .0018 | .4982 |
| 2.92 | .9982 | .0018 | .4982 |
| 2.93 | .9983 | .0017 | .4983 |
| 2.94 | .9984 | .0016 | .4984 |
| 2.95 | .9984 | .0016 | .4984 |
| 2.96 | .9985 | .0015 | .4985 |
| 2.97 | .9985 | .0015 | .4985 |
| 2.98 | .9986 | .0014 | .4986 |
| 2.99 | .9986 | .0014 | .4986 |
| 3.00 | .9987 | .0013 | .4987 |
| 3.01 | .9987 | .0013 | .4987 |
| 3.02 | .9987 | .0013 | .4987 |
| 3.03 | .9988 | .0012 | .4988 |
| 3.04 | .9988 | .0012 | .4988 |
| 3.05 | .9989 | .0011 | .4989 |
| 3.06 | .9989 | .0011 | .4989 |
| 3.07 | .9989 | .0011 | .4989 |
| 3.08 | .9990 | .0010 | .4990 |
| 3.09 | .9990 | .0010 | .4990 |
| 3.10 | .9990 | .0010 | .4990 |
| 3.11 | .9991 | .0009 | .4991 |
| 3.12 | .9991 | .0009 | .4991 |
| 3.13 | .9991 | .0009 | .4991 |
| 3.14 | .9992 | .0008 | .4992 |
| 3.15 | .9992 | .0008 | .4992 |
| 3.16 | .9992 | .0008 | .4992 |
| 3.17 | .9992 | .0008 | .4992 |
| 3.18 | .9993 | .0007 | .4993 |
| 3.19 | .9993 | .0007 | .4993 |
| 3.20 | .9993 | .0007 | .4993 |
| 3.21 | .9993 | .0007 | .4993 |
| 3.22 | .9994 | .0006 | .4994 |
| 3.23 | .9994 | .0006 | .4994 |
| 3.24 | .9994 | .0006 | .4994 |
| 3.30 | .9995 | .0005 | .4995 |
| 3.40 | .9997 | .0003 | .4997 |
| 3.50 | .9998 | .0002 | .4998 |
| 3.60 | .9998 | .0002 | .4998 |
| 3.70 | .9999 | .0001 | .4999 |
| 3.80 | .99993 | .00007 | .49993 |
| 3.90 | .99995 | .00005 | .49995 |
| 4.00 | .99997 | .00003 | .49997 |