SAT I scores around the nation tend to have a mean scale score around 500, a standard deviation of about 100 points, and are approximately normally distributed. What SAT I score within the population would have a percentile rank of approximately 99?
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion (.99) and get its Z score. Insert the Z score into the above equation to calculate the score.
To find the SAT I score within the population that would have a percentile rank of approximately 99, we can use the concept of z-scores and the standard normal distribution.
First, let's understand what a z-score represents. A z-score is a measure of how many standard deviations an individual value is from the mean of a distribution. The formula for calculating the z-score is:
z = (x - μ) / σ
Here, x represents the individual value (SAT score), μ represents the mean of the distribution, and σ represents the standard deviation.
Since the mean scale score is 500 and the standard deviation is 100, we can plug these values into the formula:
z = (x - 500) / 100
Now, to find the SAT score that corresponds to a percentile rank of approximately 99, we need to find the z-score that corresponds to the 99th percentile in the standard normal distribution. The 99th percentile is denoted as 0.99.
Using a standard normal distribution table (also known as the z-table) or a statistical calculator, we can find the z-score that corresponds to the 99th percentile. The closest z-score to the 99th percentile is approximately 2.33.
Now, we have:
2.33 = (x - 500) / 100
Solving for x:
x - 500 = 2.33 * 100
x - 500 = 233
x = 233 + 500
x = 733
Therefore, a SAT I score within the population that would have a percentile rank of approximately 99 is 733.