SATI SCORES AROUND THE NATION HAVE A MEAN SCORE AROUND 500 A STANDARD DEVIATION OF ABOUT 100 POINTS AND ARE APPROXIMATELY NORMALLY DISTRIBUTED A PERSON WHO SCORES A PERFECT SCORE OF 800 ON THE SAT I HAS APPROXIMATELY WHAT PERCENTILE RANK WITHIN THE POPULATION
First, please do not use all capitals. Online it is like SHOUTING. Not only is it rude, but it is harder to understand. Thank you.
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score.
Percentile = Proportion ≤ a score.
To determine the percentile rank of a perfect score of 800 on the SAT I within the population, we need to use the concept of standard deviation and z-scores.
First, let's calculate the z-score for a perfect score of 800. The formula for calculating the z-score is:
z = (x - μ) / σ
Where:
- x is the individual score (800 in this case)
- μ is the mean score (500 in this case)
- σ is the standard deviation (100 in this case)
Substituting the values, we get:
z = (800 - 500) / 100
z = 300 / 100
z = 3
A z-score of 3 means that the perfect score of 800 is 3 standard deviations above the mean.
Now, we can determine the percentile rank using a standardized normal distribution table or a calculator that provides the percentile based on the z-score.
Looking at a standard normal distribution table or using a calculator, we can find that a z-score of 3 corresponds to a percentile rank of approximately 99.87%.
Therefore, a person who scores a perfect score of 800 on the SAT I has approximately a percentile rank of 99.87% within the population.