5.3.2: Table of Critical Values of z

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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

Dr. MO (Taft College)
Tables modified by Michelle Oja, originally provided by Jsmura via Wikimedia Commons)