The z-table chart below illustrates this answer.įinding Areas that Fall Outside Two Z-scores We can conclude that 86.638% of values will fall within ± 1.5 standard deviations of the mean in a normally distributed population. The z-tables indicate that the areas for the higher and lower z-values are 0.93319 and 0.06681, respectively. The truncated z-tables below show the areas for z-scores of 1.5 and -1.5. However, what is the area within ± 1.5 standard deviations from the mean?

Take the larger area and subtract the smaller area from it.Īrea for Range Between Z-scores = Larger Area – Smaller Areaįor example, the empirical rule describes the areas for z-score ranges of ± 1, 2, and 3 standard deviations from the mean.

Find the area below the higher z-score.

To use a z-table to find this information, do the following: However, this process also works for ranges between any two z-scores. The number of standard deviations becomes your positive and negative z-scores. The wording might ask you to find the probability of values falling within a specified number of standard deviations from the mean. Some problems ask you to find the area between two z-scores. In other words, 25.143% of apples will weigh more than our apple. Consequently, the area above that z-score is 1 – 0.74857 = 0.25143. In this testing scenario, the result is the p-value.įor the apple example above, the z-table indicated that the area below z = 0.67 was 0.74857. Use this method to find the p-value for a one-sided z-test with the critical region in the right tail. Consequently, to find the area above a Z-score, you just need to find the area below the z-score in the z-table and subtract it from 1.Īrea above the Z-score = 1 – area below Z-score

To find areas above a z-score using a z-table, understand that the total area under the curve equals 1. The z-table chart below displays this solution visually. Alternatively, you can say that our apple is at the 74.857 th percentile. This value indicates that 74.857% of all apple weights will be lower than our apple weight of 110 grams.

The truncated z-table below shows the area for our z-score.īy looking at the intersection for 0.6 and 0.07, the z-table indicates that the area under the curve is 0.74857.

Two to twenty table chart