If you are looking to find out how to utilize the Z Score Table in order to find out the Z Score then here comes the step by step complete instruction guide about “How to Use Z-Score Table” with solved example. You can easily find out the area corresponding to a specific value of Z-Score Table.
How to Use Z-Score Table Example Question
50 randomly selected volunteers took an IQ test. Helen, one of the volunteers, scored 74 (X) from maximum possible 120 points. The average score was 62 (µ) and the standard deviation was 11 (σ). How well did she do on the test compared to other volunteers?
Step # 1 – Find the Z Score.
Firstly, you have to find out how well Helen perform in her Intelligent Test and the points of Helen needs to be converted into a z score by using the basic Z-Score Formula.
In the example, we have mentioned above, by putting values in the formula we got (74-62)/11 = 1.09090909. Simply round the value (1.09) which we called the standardized score or the Z-score. We are going to use this Z-score next.
Once you are done with the calculation of Z-Score Value or standardized score you need to look up the corresponding area by using the appropriate z-table. First of all, we have to find the 1st 2 digits on the left side of the z-table. In our case, it is 1.0. After that, we have to look up the remaining digits or numbers across the table which is 0.09 in our case. The corresponding area value is 0.8621 which actually read as 86.21%.
While on some of the Z-tables you will find the corresponding value of z-score 1.09 is 0.3621. No need to be confused at all. Such tables actually depict the area either right or left of the mean. Means that if the value is positive you need to add 0.5 (or 50%) to calculate the area to the left of z-score. And if you use that table our value become 0.3621+0.5 = 0.8621.
Step # 3 – Draw Appropriate Conclusion
The area that we gazed upward in the z-table recommends that Helen got a much better score than 86% of the volunteers who took the IQ test. In the event that you might want to know a precise number of individuals who Helen beat at the test, at that point simply increase 50 (recollect that is what number of individuals stepped through the examination) by 0.8621 which is 43.1. As there are no fractional individuals, we simply round the number to 43. Helen showed improvement over other 43 test-takers