Lastly, we take the probability associated with our upper range and subtract the probability associated with our lower range, which would be. 00 in our table, which would provide a value of. To do so, we follow the same steps and find the intersection of -1.0 and. However, we now need to find the lower bound of our range. We then find the number that corresponds to the intersection of the 1.0 row and the. We then go over to the column that includes the value of interest in the hundredth place at the top of the column. We would first find the upper bound of this range, and go to our table to find the value that corresponds to our value of interest down to the tenth place in the left-hand column.
Therefore, the probability of obtaining a z-value more than 1.0 is about 16 percent.įor the last example, let’s say that we are interested in the probability of obtaining a z-value between -1.0 and 1.0 (between one standard deviation below and above the mean). Lastly, because we are interested in the probability of obtaining a z-value greater than 1.0, we find the inverse of this probability by invoking the complement rule. Then, we would go over to the column that includes the value of interest in the hundredth place at the top of the column. We would find the value that corresponds to our value of interest down to the tenth place. We would first go to our table and again start with the left-hand column that includes numbers in the tenth place.
Therefore, the probability of obtaining a z-value less than -1.0 is about 16 percent.įor the next example, let’s say that we are interested in the probability of obtaining a z-value greater than 1.0 (one standard deviation above the mean). Lastly, we find the number that corresponds to the intersection of the -1.0 row and the. two decimal points) at the top of the column. Then, we would go over to the column that includes the value of interest in the hundredth place (e.g. To find this probability, we would go to our table and start with the left-hand column that includes numbers to the tenth place (e.g. Let’s say that we are interested in the probability of obtaining a z-value less than -1.0 (negative one standard deviation from the mean). Is it less than a certain z-value? Is it greater than a certain z-value? Is it between two z-values? To begin, we identify the range of values that we are interested in. This is because we do not want to include the probability below the lower range. Lastly, to find the probability of finding a value between two z-scores, we take the probability of finding a value below the upper range and subtract the probability of finding a value below the lower range. So, we would just take the number 1 and subtract the probability found in the table, which provides the probability of obtaining a value above the specified z-score. To find the probability of obtaining a value above a z-score, we simply invoke the complement rule (the probability of something not occurring) regarding the probability of obtaining the value below a z-score (the value found in the table). However, we can also use the table to identify the probability of obtaining a value above the z-score as well as between two z-scores. So, if we want to find the probability of obtaining a value below a certain z-score, we just find the associated z-score in the table. A z-score table identifies the probability of obtaining a value LESS THAN a certain z-score, or to the left of the value when visually observing a normal distribution. To find these probabilities, it is possible to use a z-score table. Or, it is even possible to identify the likelihood of obtaining a value between one standard deviation below and two standard deviations above the mean. Or, they might want to find the likelihood of obtaining a value that is two standard deviations above the mean. For example, someone may want to find the likelihood of obtaining a value that is one standard deviation less than the mean. These can be found in the back of most introductory statistics textbooks or performing a simple google search for a “z-value table.” If you have any questions or comments about this guide, please email me at researchers and practitioners want to identify the probability of obtaining a certain value while assuming a normal distribution in their data. This guide requires the use of a z-value table. The current page provides a guide on finding the probability associated with certain z-value ranges when assuming a normal distribution.