the average score on the statistics quiz was a 70, and there was a standard deviation of 10 points. If the z-socre was -1.0 what is the percentile rank?
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score. Percentile rank is the proportion below a particular score.
OR…
http://davidmlane.com/hyperstat/z_table.html
To find the percentile rank corresponding to a given z-score, we need to use a standard normal distribution table or a calculator.
The formula to calculate percentile rank is:
Percentile Rank = (Number of scores less than the given score / Total number of scores) * 100
In this case, if the z-score is -1.0, we want to find the percentage of scores that fall below this z-score.
Using a standard normal distribution table or a calculator, we can find that the area to the left of a z-score of -1.0 is approximately 0.1587.
To convert this to a percentile rank, we find:
Percentile Rank = 0.1587 * 100 ≈ 15.87%
Therefore, the percentile rank corresponding to a z-score of -1.0 is approximately 15.87%.
To find the percentile rank corresponding to a given z-score, follow these steps:
Step 1: Determine the area to the left of the given z-score on the standard normal distribution table.
A z-score of -1.0 corresponds to an area to the left of it. From the standard normal distribution table, you can find that the area to the left of -1.0 is approximately 0.1587.
Step 2: Convert the area to a percentile rank.
To convert the area to a percentile rank, multiply the area by 100.
Percentile Rank = 0.1587 * 100 ≈ 15.87
Therefore, the percentile rank corresponding to a z-score of -1.0 is approximately 15.87%.