Z Table - Lookup Z Score Probabilities

Find Z Tables for both negative and positive z score values, providing you with the ability to lookup z-scores by probability between 0.01 to 0.09.

Negative Z Scores Table with highlighting z score values

Negative Z Scores Table

This z-score table shows the area under the standard normal curve to the left of a given negative z-score and a probability level. Negative z scores are in the first column and probability levels in the first row.
Z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09
-3.9 0.00005 0.00005 0.00004 0.00004 0.00004 0.00004 0.00004 0.00004 0.00003 0.00003
-3.8 0.00007 0.00007 0.00007 0.00006 0.00006 0.00006 0.00006 0.00005 0.00005 0.00005
-3.7 0.00011 0.0001 0.0001 0.0001 0.00009 0.00009 0.00008 0.00008 0.00008 0.00008
-3.6 0.00016 0.00015 0.00015 0.00014 0.00014 0.00013 0.00013 0.00012 0.00012 0.00011
-3.5 0.00023 0.00022 0.00022 0.00021 0.0002 0.00019 0.00019 0.00018 0.00017 0.00017
-3.4 0.00034 0.00032 0.00031 0.0003 0.00029 0.00028 0.00027 0.00026 0.00025 0.00024
-3.3 0.00048 0.00047 0.00045 0.00043 0.00042 0.0004 0.00039 0.00038 0.00036 0.00035
-3.2 0.00069 0.00066 0.00064 0.00062 0.0006 0.00058 0.00056 0.00054 0.00052 0.0005
-3.1 0.00097 0.00094 0.0009 0.00087 0.00084 0.00082 0.00079 0.00076 0.00074 0.00071
-3.0 0.00135 0.00131 0.00126 0.00122 0.00118 0.00114 0.00111 0.00107 0.00104 0.001
-2.9 0.00187 0.00181 0.00175 0.00169 0.00164 0.00159 0.00154 0.00149 0.00144 0.00139
-2.8 0.00256 0.00248 0.0024 0.00233 0.00226 0.00219 0.00212 0.00205 0.00199 0.00193
-2.7 0.00347 0.00336 0.00326 0.00317 0.00307 0.00298 0.00289 0.0028 0.00272 0.00264
-2.6 0.00466 0.00453 0.0044 0.00427 0.00415 0.00402 0.00391 0.00379 0.00368 0.00357
-2.5 0.00621 0.00604 0.00587 0.0057 0.00554 0.00539 0.00523 0.00508 0.00494 0.0048
-2.4 0.0082 0.00798 0.00776 0.00755 0.00734 0.00714 0.00695 0.00676 0.00657 0.00639
-2.3 0.01072 0.01044 0.01017 0.0099 0.00964 0.00939 0.00914 0.00889 0.00866 0.00842
-2.2 0.0139 0.01355 0.01321 0.01287 0.01255 0.01222 0.01191 0.0116 0.0113 0.01101
-2.1 0.01786 0.01743 0.017 0.01659 0.01618 0.01578 0.01539 0.015 0.01463 0.01426
-2.0 0.02275 0.02222 0.02169 0.02118 0.02068 0.02018 0.0197 0.01923 0.01876 0.01831
-1.9 0.02872 0.02807 0.02743 0.0268 0.02619 0.02559 0.025 0.02442 0.02385 0.0233
-1.8 0.03593 0.03515 0.03438 0.03362 0.03288 0.03216 0.03144 0.03074 0.03005 0.02938
-1.7 0.04457 0.04363 0.04272 0.04182 0.04093 0.04006 0.0392 0.03836 0.03754 0.03673
-1.6 0.0548 0.0537 0.05262 0.05155 0.0505 0.04947 0.04846 0.04746 0.04648 0.04551
-1.5 0.06681 0.06552 0.06426 0.06301 0.06178 0.06057 0.05938 0.05821 0.05705 0.05592
-1.4 0.08076 0.07927 0.0778 0.07636 0.07493 0.07353 0.07215 0.07078 0.06944 0.06811
-1.3 0.0968 0.0951 0.09342 0.09176 0.09012 0.08851 0.08691 0.08534 0.08379 0.08226
-1.2 0.11507 0.11314 0.11123 0.10935 0.10749 0.10565 0.10383 0.10204 0.10027 0.09853
-1.1 0.13567 0.1335 0.13136 0.12924 0.12714 0.12507 0.12302 0.121 0.119 0.11702
-1.0 0.15866 0.15625 0.15386 0.15151 0.14917 0.14686 0.14457 0.14231 0.14007 0.13786
-0.9 0.18406 0.18141 0.17879 0.17619 0.17361 0.17106 0.16853 0.16602 0.16354 0.16109
-0.8 0.21186 0.20897 0.20611 0.20327 0.20045 0.19766 0.19489 0.19215 0.18943 0.18673
-0.7 0.24196 0.23885 0.23576 0.2327 0.22965 0.22663 0.22363 0.22065 0.2177 0.21476
-0.6 0.27425 0.27093 0.26763 0.26435 0.26109 0.25785 0.25463 0.25143 0.24825 0.2451
-0.5 0.30854 0.30503 0.30153 0.29806 0.2946 0.29116 0.28774 0.28434 0.28096 0.2776
-0.4 0.34458 0.3409 0.33724 0.3336 0.32997 0.32636 0.32276 0.31918 0.31561 0.31207
-0.3 0.38209 0.37828 0.37448 0.3707 0.36693 0.36317 0.35942 0.35569 0.35197 0.34827
-0.2 0.42074 0.41683 0.41294 0.40905 0.40517 0.40129 0.39743 0.39358 0.38974 0.38591
-0.1 0.46017 0.4562 0.45224 0.44828 0.44433 0.44038 0.43644 0.43251 0.42858 0.42465
-0.0 0.5 0.49601 0.49202 0.48803 0.48405 0.48006 0.47608 0.4721 0.46812 0.46414
Z Scores Table with highlighting z score values

Positive Z Scores Table

This z-score table shows the area under the standard normal curve to the left of a given a positive z-score. Z scores are in the first column and probability levels in the first row.
Z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09
0.0 0.5 0.50399 0.50798 0.51197 0.51595 0.51994 0.52392 0.5279 0.53188 0.53586
0.1 0.53983 0.5438 0.54776 0.55172 0.55567 0.55962 0.56356 0.56749 0.57142 0.57535
0.2 0.57926 0.58317 0.58706 0.59095 0.59483 0.59871 0.60257 0.60642 0.61026 0.61409
0.3 0.61791 0.62172 0.62552 0.6293 0.63307 0.63683 0.64058 0.64431 0.64803 0.65173
0.4 0.65542 0.6591 0.66276 0.6664 0.67003 0.67364 0.67724 0.68082 0.68439 0.68793
0.5 0.69146 0.69497 0.69847 0.70194 0.7054 0.70884 0.71226 0.71566 0.71904 0.7224
0.6 0.72575 0.72907 0.73237 0.73565 0.73891 0.74215 0.74537 0.74857 0.75175 0.7549
0.7 0.75804 0.76115 0.76424 0.7673 0.77035 0.77337 0.77637 0.77935 0.7823 0.78524
0.8 0.78814 0.79103 0.79389 0.79673 0.79955 0.80234 0.80511 0.80785 0.81057 0.81327
0.9 0.81594 0.81859 0.82121 0.82381 0.82639 0.82894 0.83147 0.83398 0.83646 0.83891
1.0 0.84134 0.84375 0.84614 0.84849 0.85083 0.85314 0.85543 0.85769 0.85993 0.86214
1.1 0.86433 0.8665 0.86864 0.87076 0.87286 0.87493 0.87698 0.879 0.881 0.88298
1.2 0.88493 0.88686 0.88877 0.89065 0.89251 0.89435 0.89617 0.89796 0.89973 0.90147
1.3 0.9032 0.9049 0.90658 0.90824 0.90988 0.91149 0.91309 0.91466 0.91621 0.91774
1.4 0.91924 0.92073 0.9222 0.92364 0.92507 0.92647 0.92785 0.92922 0.93056 0.93189
1.5 0.93319 0.93448 0.93574 0.93699 0.93822 0.93943 0.94062 0.94179 0.94295 0.94408
1.6 0.9452 0.9463 0.94738 0.94845 0.9495 0.95053 0.95154 0.95254 0.95352 0.95449
1.7 0.95543 0.95637 0.95728 0.95818 0.95907 0.95994 0.9608 0.96164 0.96246 0.96327
1.8 0.96407 0.96485 0.96562 0.96638 0.96712 0.96784 0.96856 0.96926 0.96995 0.97062
1.9 0.97128 0.97193 0.97257 0.9732 0.97381 0.97441 0.975 0.97558 0.97615 0.9767
2.0 0.97725 0.97778 0.97831 0.97882 0.97932 0.97982 0.9803 0.98077 0.98124 0.98169
2.1 0.98214 0.98257 0.983 0.98341 0.98382 0.98422 0.98461 0.985 0.98537 0.98574
2.2 0.9861 0.98645 0.98679 0.98713 0.98745 0.98778 0.98809 0.9884 0.9887 0.98899
2.3 0.98928 0.98956 0.98983 0.9901 0.99036 0.99061 0.99086 0.99111 0.99134 0.99158
2.4 0.9918 0.99202 0.99224 0.99245 0.99266 0.99286 0.99305 0.99324 0.99343 0.99361
2.5 0.99379 0.99396 0.99413 0.9943 0.99446 0.99461 0.99477 0.99492 0.99506 0.9952
2.6 0.99534 0.99547 0.9956 0.99573 0.99585 0.99598 0.99609 0.99621 0.99632 0.99643
2.7 0.99653 0.99664 0.99674 0.99683 0.99693 0.99702 0.99711 0.9972 0.99728 0.99736
2.8 0.99744 0.99752 0.9976 0.99767 0.99774 0.99781 0.99788 0.99795 0.99801 0.99807
2.9 0.99813 0.99819 0.99825 0.99831 0.99836 0.99841 0.99846 0.99851 0.99856 0.99861
3.0 0.99865 0.99869 0.99874 0.99878 0.99882 0.99886 0.99889 0.99893 0.99896 0.999
3.1 0.99903 0.99906 0.9991 0.99913 0.99916 0.99918 0.99921 0.99924 0.99926 0.99929
3.2 0.99931 0.99934 0.99936 0.99938 0.9994 0.99942 0.99944 0.99946 0.99948 0.9995
3.3 0.99952 0.99953 0.99955 0.99957 0.99958 0.9996 0.99961 0.99962 0.99964 0.99965
3.4 0.99966 0.99968 0.99969 0.9997 0.99971 0.99972 0.99973 0.99974 0.99975 0.99976
3.5 0.99977 0.99978 0.99978 0.99979 0.9998 0.99981 0.99981 0.99982 0.99983 0.99983
3.6 0.99984 0.99985 0.99985 0.99986 0.99986 0.99987 0.99987 0.99988 0.99988 0.99989
3.7 0.99989 0.9999 0.9999 0.9999 0.99991 0.99991 0.99992 0.99992 0.99992 0.99992
3.8 0.99993 0.99993 0.99993 0.99994 0.99994 0.99994 0.99994 0.99995 0.99995 0.99995
3.9 0.99995 0.99995 0.99996 0.99996 0.99996 0.99996 0.99996 0.99996 0.99997 0.99997

Understanding Z-Tables: A Guide to Using Z-Scores in Statistical Analysis

In statistics, a z-table, also known as a standard normal distribution table, is a tool used to find the area under the standard normal distribution curve. The standard normal distribution has a mean of 0 and a standard deviation of 1, making it a useful reference distribution for many statistical calculations. In this article, we will explore how to use a z-table, its applications, and examples of its usage.

What is a Z-Table?

A z-table is a table of values that correspond to the area under the standard normal distribution curve for a given z-score. The z-score is a standard score that represents the number of standard deviations a data point is from the mean of the distribution. A z-score of 0 represents a data point at the mean, while a positive or negative z-score represents a data point above or below the mean, respectively.

Using a Z-Table

To use a z-table, you first need to know the z-score for the data point of interest. Once you have the z-score, locate the row and column on the z-table that correspond to the tenths and hundredths digit of the z-score, respectively. The value at the intersection of the row and column represents the area under the standard normal distribution curve to the left of the z-score.

Applications of a Z-Table

Z-tables are commonly used in hypothesis testing, confidence interval estimation, and statistical modeling. In hypothesis testing, the z-score is used to calculate the p-value, which represents the probability of observing a result as extreme as the one observed, assuming the null hypothesis is true. The p-value is then compared to the significance level to determine whether to reject or fail to reject the null hypothesis.

In confidence interval estimation, the z-score is used to calculate the margin of error for the estimate. The margin of error is the range within which the true population parameter is expected to fall with a certain level of confidence.

Examples of Using a Z-Table

Example 1: Suppose you have a z-score of 1.50. Using a z-table, you can find that the area to the left of this z-score is 0.9332. This means that 93.32% of the values in the distribution are below the z-score of 1.50.

Example 2: Suppose you want to find the z-score that corresponds to the 90th percentile of the distribution. Using a z-table, you can find that the z-score is approximately 1.28. This means that 90% of the values in the distribution are below the z-score of 1.28.

Example 3: A company has a customer satisfaction score with a mean of 75 and a standard deviation of 10. Suppose a customer scores 85. Using a z-table, you can find that the z-score is 1.0, indicating that the customer's score is one standard deviation above the mean.

Example 4: A teacher grades a test with a mean score of 75 and a standard deviation of 5. Suppose a student scores 85. Using a z-table, you can find that the z-score is 2.0, indicating that the student's score is two standard deviations above the mean.

Example 5: A manufacturing company produces a product with a mean weight of 10 ounces and a standard deviation of 0.5 ounces. Suppose a batch of products has a weight of 9.5 ounces. Using a z-table, you can find that the z-score is -1.0, indicating that the batch's weight is one standard deviation below the mean.

Example 6: An athlete's performance is compared to the average performance of all athletes in their sport. Suppose the athlete's performance is two standard deviations above the mean. Using a z-table, you can find that the z-score is approximately 2.0, indicating that the athlete's performance is better than 97.72% of all other athletes in their sport.

Example 7: A survey is conducted to measure the average income of households in a city. The data collected has a mean of $60,000 and a standard deviation of $8,000. Suppose a household has an income of $72,000. Using a z-table, you can find that the z-score is 1.5, indicating that the household's income is one and a half standard deviations above the mean.

Example 8: A study is conducted to measure the effectiveness of a new medication. The data collected has a mean effectiveness rate of 80% with a standard deviation of 5%. Suppose the medication is found to have an effectiveness rate of 90%. Using a z-table, you can find that the z-score is 2, indicating that the effectiveness rate of the medication is two standard deviations above the mean.

Example 9: A company wants to measure the heights of its employees. The collected data has a mean of 5'9'' and a standard deviation of 3 inches. Suppose an employee's height is 6'3''. Using a z-table, you can find that the z-score is 1, indicating that the employee's height is one standard deviation above the mean.

In summary, a z-table is an essential tool for those working with statistical data. It provides a simple and effective way to find the area under the standard normal distribution curve for a given z-score. This allows for more precise hypothesis testing, confidence interval estimation, and statistical modeling.

By using a z-table, you can quickly determine the probability associated with a particular z-score, making it easier to interpret and draw conclusions from statistical data. It is essential to understand how to use a z-table correctly, as errors in calculation or interpretation can lead to incorrect conclusions.

Overall, the z-table is a valuable tool that should be part of any statistical analysis toolkit. Whether you are a student, researcher, or working professional, understanding the principles behind the z-table and how to use it can help you make more informed decisions when analyzing data.