sat scores around the nation tend to have a mean score of about 500, a standard deviation of 100 points and are approximately normal distribution. a person who score 600 on the sat has approximately what percentile rank within the population? show all calculations.
600-500/100=-100/100=0.999999
*this is what i can up with, can anyone tell me if i am correct. if not show how the calculation should be made. thank you.
See:
http://www.jiskha.com/display.cgi?id=1287253893
To determine the percentile rank of a score within a normal distribution, you need to calculate the z-score, which represents the number of standard deviations the score is from the mean.
To calculate the z-score for a score of 600 in this case:
z = (x - μ) / σ
Where:
x = the score (600)
μ = the mean (500)
σ = the standard deviation (100)
Plugging in the values:
z = (600 - 500) / 100
z = 1
The z-score of 1 indicates that the score of 600 is 1 standard deviation above the mean.
Now, you can determine the percentile rank using a z-table (also known as a standard normal distribution table) or a calculator that has a built-in function to calculate percentiles for a normal distribution.
In this case, if you're using a z-table, you would find the area (or percentile) to the left of z = 1. This area corresponds to the percentile rank of 84.13%.
Therefore, a score of 600 on the SAT would have an approximate percentile rank of 84.13% within the population.