Z Score Table

CLINICAL BIOSTATS

The standard normal table, also known as the z-score table, is a mathematical tool used to determine the cumulative distribution function values of the normal distribution. It allows us to find the probabilities associated with different z-scores. The z-score, which represents the number of standard deviations an entity is from the mean, is a way to compare results to a “normal” population.

Since it is not feasible to create probability tables for every possible normal distribution, a common practice is to convert the normal distribution to a standard normal distribution using the z-score. The z-score is calculated by subtracting the mean from the test value and dividing the result by the standard deviation:

Z-Score Formula

Where:

z is the z-score.

x is the observed value.

μ is the mean of the population.

σ is the standard deviation of the population.

Interpreting z-scores follows a simple guideline:

A z-score greater than 0 indicates an element above the mean.
A z-score of 0 represents an element equal to the mean.
A z-score of 1 signifies an element that is one standard deviation above the mean.
A z-score of 2 indicates two standard deviations above the mean, and so on.
Similarly, a z-score of -1 represents an element one standard deviation below the mean.
A z-score of -2 signifies two standard deviations below the mean, and so on.

For a large set of elements, approximately:

68% of the elements have a z-score between -1 and 1.

95% have a z-score between -2 and 2.

99% have a z-score between -3 and 3.

Understanding and utilizing z-scores and the standard normal table can provide valuable insights when analyzing data and comparing it to a standard population.

Normal Distribution PDF Formula

The probability density function (PDF) for a normal distribution is given by:

In the above formula:

μ represents the mean of the distribution.
σ represents the standard deviation of the distribution.
e is the base of the natural logarithm.

μ represents the mean of the distribution.σ represents the standard deviation of the distribution.e is the base of the natural logarithm.π is the mathematical constant pi (approximately 3.14159).

Normal Distribution CDF Formula

The cumulative density function (PDF) for a normal distribution is given by:

In the above formula:

μ represents the mean of the distribution.
σ represents the standard deviation of the distribution.
erf(z) is the error function, which calculates the integral of the standard normal distribution from -∞ to z.
√(2) is the square root of 2

Z	.00	.01	.02	.03	.04	.05	.06	.07	.08	.09
-4.90	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000
-4.80	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000
-4.70	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000
-4.60	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000
-4.50	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000
-4.40	0.00001	0.00001	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000
-4.30	0.00001	0.00001	0.00001	0.00001	0.00001	0.00001	0.00001	0.00001	0.00001	0.00001
-4.20	0.00001	0.00001	0.00001	0.00001	0.00001	0.00001	0.00001	0.00001	0.00001	0.00001
-4.10	0.00002	0.00002	0.00002	0.00002	0.00002	0.00002	0.00002	0.00002	0.00001	0.00001
-4.00	0.00003	0.00003	0.00003	0.00003	0.00003	0.00003	0.00002	0.00002	0.00002	0.00002
-3.90	0.00005	0.00005	0.00004	0.00004	0.00004	0.00004	0.00004	0.00004	0.00003	0.00003
-3.80	0.00007	0.00007	0.00007	0.00006	0.00006	0.00006	0.00006	0.00005	0.00005	0.00005
-3.70	0.00011	0.00010	0.00010	0.00010	0.00009	0.00009	0.00008	0.00008	0.00008	0.00008
-3.60	0.00016	0.00015	0.00015	0.00014	0.00014	0.00013	0.00013	0.00012	0.00012	0.00011
-3.50	0.00023	0.00022	0.00022	0.00021	0.00020	0.00019	0.00019	0.00018	0.00017	0.00017
-3.40	0.00034	0.00032	0.00031	0.00030	0.00029	0.00028	0.00027	0.00026	0.00025	0.00024
-3.30	0.00048	0.00047	0.00045	0.00043	0.00042	0.00040	0.00039	0.00038	0.00036	0.00035
-3.20	0.00069	0.00066	0.00064	0.00062	0.00060	0.00058	0.00056	0.00054	0.00052	0.00050
-3.10	0.00097	0.00094	0.00090	0.00087	0.00084	0.00082	0.00079	0.00076	0.00074	0.00071
-3.00	0.00135	0.00131	0.00126	0.00122	0.00118	0.00114	0.00111	0.00107	0.00104	0.00100
-2.90	0.00187	0.00181	0.00175	0.00169	0.00164	0.00159	0.00154	0.00149	0.00144	0.00139
-2.80	0.00256	0.00248	0.00240	0.00233	0.00226	0.00219	0.00212	0.00205	0.00199	0.00193
-2.70	0.00347	0.00336	0.00326	0.00317	0.00307	0.00298	0.00289	0.00280	0.00272	0.00264
-2.60	0.00466	0.00453	0.00440	0.00427	0.00415	0.00402	0.00391	0.00379	0.00368	0.00357
-2.50	0.00621	0.00604	0.00587	0.00570	0.00554	0.00539	0.00523	0.00508	0.00494	0.00480
-2.40	0.00820	0.00798	0.00776	0.00755	0.00734	0.00714	0.00695	0.00676	0.00657	0.00639
-2.30	0.01072	0.01044	0.01017	0.00990	0.00964	0.00939	0.00914	0.00889	0.00866	0.00842
-2.20	0.01390	0.01355	0.01321	0.01287	0.01255	0.01222	0.01191	0.01160	0.01130	0.01101
-2.10	0.01786	0.01743	0.01700	0.01659	0.01618	0.01578	0.01539	0.01500	0.01463	0.01426
-2.00	0.02275	0.02222	0.02169	0.02118	0.02068	0.02018	0.01970	0.01923	0.01876	0.01831
-1.90	0.02872	0.02807	0.02743	0.02680	0.02619	0.02559	0.02500	0.02442	0.02385	0.02330
-1.80	0.03593	0.03515	0.03438	0.03362	0.03288	0.03216	0.03144	0.03074	0.03005	0.02938
-1.70	0.04457	0.04363	0.04272	0.04182	0.04093	0.04006	0.03920	0.03836	0.03754	0.03673
-1.60	0.05480	0.05370	0.05262	0.05155	0.05050	0.04947	0.04846	0.04746	0.04648	0.04551
-1.50	0.06681	0.06552	0.06426	0.06301	0.06178	0.06057	0.05938	0.05821	0.05705	0.05592
-1.40	0.08076	0.07927	0.07780	0.07636	0.07493	0.07353	0.07215	0.07078	0.06944	0.06811
-1.30	0.09680	0.09510	0.09342	0.09176	0.09012	0.08851	0.08691	0.08534	0.08379	0.08226
-1.20	0.11507	0.11314	0.11123	0.10935	0.10749	0.10565	0.10383	0.10204	0.10027	0.09853
-1.10	0.13567	0.13350	0.13136	0.12924	0.12714	0.12507	0.12302	0.12100	0.11900	0.11702
-1.00	0.15866	0.15625	0.15386	0.15151	0.14917	0.14686	0.14457	0.14231	0.14007	0.13786
-0.90	0.18406	0.18141	0.17879	0.17619	0.17361	0.17106	0.16853	0.16602	0.16354	0.16109
-0.80	0.21186	0.20897	0.20611	0.20327	0.20045	0.19766	0.19489	0.19215	0.18943	0.18673
-0.70	0.24196	0.23885	0.23576	0.23270	0.22965	0.22663	0.22363	0.22065	0.21770	0.21476
-0.60	0.27425	0.27093	0.26763	0.26435	0.26109	0.25785	0.25463	0.25143	0.24825	0.24510
-0.50	0.30854	0.30503	0.30153	0.29806	0.29460	0.29116	0.28774	0.28434	0.28096	0.27760
-0.40	0.34458	0.34090	0.33724	0.33360	0.32997	0.32636	0.32276	0.31918	0.31561	0.31207
-0.30	0.38209	0.37828	0.37448	0.37070	0.36693	0.36317	0.35942	0.35569	0.35197	0.34827
-0.20	0.42074	0.41683	0.41294	0.40905	0.40517	0.40129	0.39743	0.39358	0.38974	0.38591
-0.10	0.46017	0.45620	0.45224	0.44828	0.44433	0.44038	0.43644	0.43251	0.42858	0.42465
-0.00	0.50000	0.49601	0.49202	0.48803	0.48405	0.48006	0.47608	0.47210	0.46812	0.46414

Z	.00	.01	.02	.03	.04	.05	.06	.07	.08	.09
0.00	0.50000	0.50399	0.50798	0.51197	0.51595	0.51994	0.52392	0.52790	0.53188	0.53586
0.10	0.53983	0.54380	0.54776	0.55172	0.55567	0.55962	0.56356	0.56749	0.57142	0.57535
0.20	0.57926	0.58317	0.58706	0.59095	0.59483	0.59871	0.60257	0.60642	0.61026	0.61409
0.30	0.61791	0.62172	0.62552	0.62930	0.63307	0.63683	0.64058	0.64431	0.64803	0.65173
0.40	0.65542	0.65910	0.66276	0.66640	0.67003	0.67364	0.67724	0.68082	0.68439	0.68793
0.50	0.69146	0.69497	0.69847	0.70194	0.70540	0.70884	0.71226	0.71566	0.71904	0.72240
0.60	0.72575	0.72907	0.73237	0.73565	0.73891	0.74215	0.74537	0.74857	0.75175	0.75490
0.70	0.75804	0.76115	0.76424	0.76730	0.77035	0.77337	0.77637	0.77935	0.78230	0.78524
0.80	0.78814	0.79103	0.79389	0.79673	0.79955	0.80234	0.80511	0.80785	0.81057	0.81327
0.90	0.81594	0.81859	0.82121	0.82381	0.82639	0.82894	0.83147	0.83398	0.83646	0.83891
1.00	0.84134	0.84375	0.84614	0.84849	0.85083	0.85314	0.85543	0.85769	0.85993	0.86214
1.10	0.86433	0.86650	0.86864	0.87076	0.87286	0.87493	0.87698	0.87900	0.88100	0.88298
1.20	0.88493	0.88686	0.88877	0.89065	0.89251	0.89435	0.89617	0.89796	0.89973	0.90147
1.30	0.90320	0.90490	0.90658	0.90824	0.90988	0.91149	0.91309	0.91466	0.91621	0.91774
1.40	0.91924	0.92073	0.92220	0.92364	0.92507	0.92647	0.92785	0.92922	0.93056	0.93189
1.50	0.93319	0.93448	0.93574	0.93699	0.93822	0.93943	0.94062	0.94179	0.94295	0.94408
1.60	0.94520	0.94630	0.94738	0.94845	0.94950	0.95053	0.95154	0.95254	0.95352	0.95449
1.70	0.95543	0.95637	0.95728	0.95818	0.95907	0.95994	0.96080	0.96164	0.96246	0.96327
1.80	0.96407	0.96485	0.96562	0.96638	0.96712	0.96784	0.96856	0.96926	0.96995	0.97062
1.90	0.97128	0.97193	0.97257	0.97320	0.97381	0.97441	0.97500	0.97558	0.97615	0.97670
2.00	0.97725	0.97778	0.97831	0.97882	0.97932	0.97982	0.98030	0.98077	0.98124	0.98169
2.10	0.98214	0.98257	0.98300	0.98341	0.98382	0.98422	0.98461	0.98500	0.98537	0.98574
2.20	0.98610	0.98645	0.98679	0.98713	0.98745	0.98778	0.98809	0.98840	0.98870	0.98899
2.30	0.98928	0.98956	0.98983	0.99010	0.99036	0.99061	0.99086	0.99111	0.99134	0.99158
2.40	0.99180	0.99202	0.99224	0.99245	0.99266	0.99286	0.99305	0.99324	0.99343	0.99361
2.50	0.99379	0.99396	0.99413	0.99430	0.99446	0.99461	0.99477	0.99492	0.99506	0.99520
2.60	0.99534	0.99547	0.99560	0.99573	0.99585	0.99598	0.99609	0.99621	0.99632	0.99643
2.70	0.99653	0.99664	0.99674	0.99683	0.99693	0.99702	0.99711	0.99720	0.99728	0.99736
2.80	0.99744	0.99752	0.99760	0.99767	0.99774	0.99781	0.99788	0.99795	0.99801	0.99807
2.90	0.99813	0.99819	0.99825	0.99831	0.99836	0.99841	0.99846	0.99851	0.99856	0.99861
3.00	0.99865	0.99869	0.99874	0.99878	0.99882	0.99886	0.99889	0.99893	0.99896	0.99900
3.10	0.99903	0.99906	0.99910	0.99913	0.99916	0.99918	0.99921	0.99924	0.99926	0.99929
3.20	0.99931	0.99934	0.99936	0.99938	0.99940	0.99942	0.99944	0.99946	0.99948	0.99950
3.30	0.99952	0.99953	0.99955	0.99957	0.99958	0.99960	0.99961	0.99962	0.99964	0.99965
3.40	0.99966	0.99968	0.99969	0.99970	0.99971	0.99972	0.99973	0.99974	0.99975	0.99976
3.50	0.99977	0.99978	0.99978	0.99979	0.99980	0.99981	0.99981	0.99982	0.99983	0.99983
3.60	0.99984	0.99985	0.99985	0.99986	0.99986	0.99987	0.99987	0.99988	0.99988	0.99989
3.70	0.99989	0.99990	0.99990	0.99990	0.99991	0.99991	0.99992	0.99992	0.99992	0.99992
3.80	0.99993	0.99993	0.99993	0.99994	0.99994	0.99994	0.99994	0.99995	0.99995	0.99995
3.90	0.99995	0.99995	0.99996	0.99996	0.99996	0.99996	0.99996	0.99996	0.99997	0.99997
4.00	0.99997	0.99997	0.99997	0.99997	0.99997	0.99997	0.99998	0.99998	0.99998	0.99998
4.10	0.99998	0.99998	0.99998	0.99998	0.99998	0.99998	0.99998	0.99998	0.99999	0.99999
4.20	0.99999	0.99999	0.99999	0.99999	0.99999	0.99999	0.99999	0.99999	0.99999	0.99999
4.30	0.99999	0.99999	0.99999	0.99999	0.99999	0.99999	0.99999	0.99999	0.99999	0.99999
4.40	0.99999	0.99999	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
4.50	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
4.60	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
4.70	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
4.80	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
4.90	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000

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Z Score Table - Clinical Biostats (2024)

FAQs

What is the z-score in biostatistics? ›

A z-score in statistics is defined as the number of standard deviations of a value from the mean of its distribution. It is a score used to standardize any distribution so that it can be directly compared with others, though it is usually used with normal distributions.

Learn More Now ›

What is a reasonable z-score? ›

What Is a Good Z-Score? 0 is used as the mean and indicates average Z-scores. Any positive Z-score is a good, standard score. However, a larger Z-score of around 3 shows strong financial stability and would be considered above the standard score.

Is a higher z-score better? ›

What Is a Good Z-Score? The higher (or lower) a z-score is, the further away from the mean the point is. This isn't necessarily good or bad; it merely shows where the data lies in a normally distributed sample. This means it comes down to preference when evaluating an investment or opportunity.

Discover More Details ›

What is the z-score in medical statistics? ›

According to the Bone Health and Osteoporosis Foundation (BHOF), Z-scores compare a person's bone density with the average bone density of those of the same age, sex, and body size. These scores are in the form of standard deviations. This mathematical term measures how close a number is to the average.

Keep Reading ›

What is a healthy z-score? ›

Z-score results

Z-score range	Description
-1.5 and above	typical bone density for peer group
Lower than -1.5	atypical BMD, needs investigation

Feb 21, 2023

Discover More ›

What is a safe z-score? ›

A Z-score that is lower than 1.8 means that the company is in financial distress and with a high probability of going bankrupt. On the other hand, a score of 3 and above means that the company is in a safe zone and is unlikely to file for bankruptcy.

Know More ›

What is considered an abnormal z-score? ›

A standard normal curve, in general, is a bell-shaped curve. So, the scores that are lower than -1.96 or higher than 1.96 are considered as unusual z-scores.

Read On ›

How to interpret z-score? ›

A Z-score of 2.5 means your observed value is 2.5 standard deviations from the mean and so on. The closer your Z-score is to zero, the closer your value is to the mean. The further away your Z-score is from zero, the further away your value is from the mean.

Keep Reading ›

What is the difference between Z table and T table? ›

What's the key difference between the t- and z-distributions? The standard normal or z-distribution assumes that you know the population standard deviation. The t-distribution is based on the sample standard deviation.

Tell Me More ›

What is the easiest way to find the z-score? ›

If you know the mean and standard deviation, you can find the z-score using the formula z = (x - μ) / σ where x is your data point, μ is the mean, and σ is the standard deviation.

Keep Reading ›

What does Z stand for in biostatistics? ›

What Is a Z-Score? A z-score, or z-statistic, is a number representing how many standard deviations above or below the mean population the score derived from a z-test is. Essentially, it is a numerical measurement that describes a value's relationship to the mean of a group of values.

How do you interpret the z-score? ›

Z-scores can be positive or negative. The sign tells you whether the observation is above or below the mean. For example, a z-score of +2 indicates that the data point falls two standard deviations above the mean, while a -2 signifies it is two standard deviations below the mean. A z-score of zero equals the mean.

Read The Full Story ›

What is 95% z-score? ›

The critical z-score values when using a 95 percent confidence level are -1.96 and +1.96 standard deviations. The uncorrected p-value associated with a 95 percent confidence level is 0.05.

What is the normal Z in statistics? ›

A z-score of 0 indicates that the given point is identical to the mean. On the graph of the standard normal distribution, z = 0 is therefore the center of the curve. A positive z-value indicates that the point lies to the right of the mean, and a negative z-value indicates that the point lies left of the mean.

Keep Reading ›

Z Score Table - Clinical Biostats (2024)

CLINICAL BIOSTATS

Z Score Table

Z Score Table

Where:

z is the z-score.

x is the observed value.

μ is the mean of the population.

σ is the standard deviation of the population.

Interpreting z-scores follows a simple guideline:

A z-score greater than 0 indicates an element above the mean.

A z-score of 0 represents an element equal to the mean.

A z-score of 1 signifies an element that is one standard deviation above the mean.

A z-score of 2 indicates two standard deviations above the mean, and so on.

Similarly, a z-score of -1 represents an element one standard deviation below the mean.

A z-score of -2 signifies two standard deviations below the mean, and so on.

For a large set of elements, approximately:

68% of the elements have a z-score between -1 and 1.

95% have a z-score between -2 and 2.

99% have a z-score between -3 and 3.

Understanding and utilizing z-scores and the standard normal table can provide valuable insights when analyzing data and comparing it to a standard population.

Normal Distribution PDF Formula

The probability density function (PDF) for a normal distribution is given by:

In the above formula:

μ represents the mean of the distribution.

σ represents the standard deviation of the distribution.

e is the base of the natural logarithm.

μ represents the mean of the distribution.σ represents the standard deviation of the distribution.e is the base of the natural logarithm.π is the mathematical constant pi (approximately 3.14159).

Normal Distribution CDF Formula

The cumulative density function (PDF) for a normal distribution is given by:

In the above formula:

μ represents the mean of the distribution.

σ represents the standard deviation of the distribution.

erf(z) is the error function, which calculates the integral of the standard normal distribution from -∞ to z.

√(2) is the square root of 2

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What is the z-score in biostatistics? ›

What does Z stand for in biostatistics? ›

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