Question 1

How do I read a z-score table?

Accepted Answer

Find the row matching the first two digits of your z-score (e.g., 1.9 for z = 1.96), then move across to the column matching the hundredths digit (0.06). The intersection gives P(Z ≤ z). For z = 1.96: row 1.9, column 0.06 → 0.9750, meaning 97.50% of values fall below z = 1.96.

Question 2

What is the z-score table used for?

Accepted Answer

The z-table gives the cumulative probability P(Z ≤ z) for a standard normal distribution. It is used in hypothesis testing to find p-values, in confidence intervals to find critical values (e.g., z = 1.96 for 95% CI), and in quality control (six sigma). Any normally distributed data can be converted to a z-score and looked up in this table.

Question 3

What does P(Z ≤ z) mean?

Accepted Answer

P(Z ≤ z) is the probability that a standard normal random variable Z is less than or equal to the value z. It represents the area under the normal curve to the left of z. For example, P(Z ≤ 1.96) = 0.9750 means there is a 97.50% chance a random value falls below z = 1.96.

Question 4

What is the z-score for 95% confidence?

Accepted Answer

For a 95% confidence interval (two-tailed), the critical z-value is 1.960. This means 95% of the area under the standard normal curve falls between −1.96 and +1.96. For a one-tailed 95% test, use z = 1.645.

Question 5

How do I find the probability between two z-scores?

Accepted Answer

Subtract the smaller probability from the larger. Example: P(−1.96 ≤ Z ≤ 1.96) = P(Z ≤ 1.96) − P(Z ≤ −1.96) = 0.9750 − 0.0250 = 0.9500, confirming 95% of values fall within 1.96 standard deviations of the mean.

Question 6

What is the z-score for p = 0.05 (significance level)?

Accepted Answer

For a one-tailed test at α = 0.05, the critical z-value is 1.645 (reject H₀ if z > 1.645). For a two-tailed test at α = 0.05, the critical value is ±1.960. These are the most commonly used critical values in statistics.

Confidence Level	α (one-tail)	α (two-tail)	Critical z
80%	0.10	0.20	±1.282
85%	0.075	0.15	±1.440
90%	0.05	0.10	±1.645
95%	0.025	0.05	±1.960
97.5%	0.0125	0.025	±2.241
99%	0.005	0.01	±2.576
99.5%	0.0025	0.005	±2.807
99.9%	0.0005	0.001	±3.291

z	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0	0.5000	0.5040	0.5080	0.5120	0.5160	0.5199	0.5239	0.5279	0.5319	0.5359
0.1	0.5398	0.5438	0.5478	0.5517	0.5557	0.5596	0.5636	0.5675	0.5714	0.5753
0.2	0.5793	0.5832	0.5871	0.5910	0.5948	0.5987	0.6026	0.6064	0.6103	0.6141
0.3	0.6179	0.6217	0.6255	0.6293	0.6331	0.6368	0.6406	0.6443	0.6480	0.6517
0.4	0.6554	0.6591	0.6628	0.6664	0.6700	0.6736	0.6772	0.6808	0.6844	0.6879
0.5	0.6915	0.6950	0.6985	0.7019	0.7054	0.7088	0.7123	0.7157	0.7190	0.7224
0.6	0.7257	0.7291	0.7324	0.7357	0.7389	0.7422	0.7454	0.7486	0.7517	0.7549
0.7	0.7580	0.7611	0.7642	0.7673	0.7704	0.7734	0.7764	0.7794	0.7823	0.7852
0.8	0.7881	0.7910	0.7939	0.7967	0.7995	0.8023	0.8051	0.8078	0.8106	0.8133
0.9	0.8159	0.8186	0.8212	0.8238	0.8264	0.8289	0.8315	0.8340	0.8365	0.8389
1.0	0.8413	0.8438	0.8461	0.8485	0.8508	0.8531	0.8554	0.8577	0.8599	0.8621
1.1	0.8643	0.8665	0.8686	0.8708	0.8729	0.8749	0.8770	0.8790	0.8810	0.8830
1.2	0.8849	0.8869	0.8888	0.8907	0.8925	0.8944	0.8962	0.8980	0.8997	0.9015
1.3	0.9032	0.9049	0.9066	0.9082	0.9099	0.9115	0.9131	0.9147	0.9162	0.9177
1.4	0.9192	0.9207	0.9222	0.9236	0.9251	0.9265	0.9279	0.9292	0.9306	0.9319
1.5	0.9332	0.9345	0.9357	0.9370	0.9382	0.9394	0.9406	0.9418	0.9429	0.9441
1.6	0.9452	0.9463	0.9474	0.9484	0.9495	0.9505	0.9515	0.9525	0.9535	0.9545
1.7	0.9554	0.9564	0.9573	0.9582	0.9591	0.9599	0.9608	0.9616	0.9625	0.9633
1.8	0.9641	0.9649	0.9656	0.9664	0.9671	0.9678	0.9686	0.9693	0.9699	0.9706
1.9	0.9713	0.9719	0.9726	0.9732	0.9738	0.9744	0.9750	0.9756	0.9761	0.9767
2.0	0.9772	0.9778	0.9783	0.9788	0.9793	0.9798	0.9803	0.9808	0.9812	0.9817
2.1	0.9821	0.9826	0.9830	0.9834	0.9838	0.9842	0.9846	0.9850	0.9854	0.9857
2.2	0.9861	0.9864	0.9868	0.9871	0.9875	0.9878	0.9881	0.9884	0.9887	0.9890
2.3	0.9893	0.9896	0.9898	0.9901	0.9904	0.9906	0.9909	0.9911	0.9913	0.9916
2.4	0.9918	0.9920	0.9922	0.9925	0.9927	0.9929	0.9931	0.9932	0.9934	0.9936
2.5	0.9938	0.9940	0.9941	0.9943	0.9945	0.9946	0.9948	0.9949	0.9951	0.9952
2.6	0.9953	0.9955	0.9956	0.9957	0.9959	0.9960	0.9961	0.9962	0.9963	0.9964
2.7	0.9965	0.9966	0.9967	0.9968	0.9969	0.9970	0.9971	0.9972	0.9973	0.9974
2.8	0.9974	0.9975	0.9976	0.9977	0.9977	0.9978	0.9979	0.9979	0.9980	0.9981
2.9	0.9981	0.9982	0.9982	0.9983	0.9984	0.9984	0.9985	0.9985	0.9986	0.9986
3.0	0.9987	0.9987	0.9987	0.9988	0.9988	0.9989	0.9989	0.9989	0.9990	0.9990
3.1	0.9990	0.9991	0.9991	0.9991	0.9992	0.9992	0.9992	0.9992	0.9993	0.9993
3.2	0.9993	0.9993	0.9994	0.9994	0.9994	0.9994	0.9994	0.9995	0.9995	0.9995
3.3	0.9995	0.9995	0.9995	0.9996	0.9996	0.9996	0.9996	0.9996	0.9996	0.9997
3.4	0.9997	0.9997	0.9997	0.9997	0.9997	0.9997	0.9997	0.9997	0.9997	0.9998

Z-Score Table

Quick Z-Score Lookup

Critical Z-Values — Quick Reference

Positive Z-Table — P(Z ≤ z)

How to Read the Z-Table

Empirical Rule (68–95–99.7)

Common Uses for the Z-Table

Hypothesis Testing (p-values)

Confidence Intervals

Percentile Calculation

Quality Control (Six Sigma)

Related Statistics Tools

Frequently Asked Questions