IF SAT scores have approximately a normal distribution with the mean being 550 and standard deviation of 90. How can I calculate the SAT scores of the 95th percentile?
Thank you
http://davidmlane.com/hyperstat/z_table.html
check AREA box
put in
Area = .05
result is 95 % are below 698
To calculate the SAT scores corresponding to the 95th percentile, you can follow these steps:
1. Convert the percentile to a z-score: The z-score represents the number of standard deviations an observation is from the mean. The formula to calculate the z-score is given by:
z = (X - μ) / σ
where X is the value we want to find (in this case, the SAT score at the 95th percentile), μ is the mean (550 in this case), and σ is the standard deviation (90 in this case).
2. Use a z-table or a calculator: Look up the z-score corresponding to the 95th percentile using a z-table or use a calculator that can compute z-scores and percentiles.
In this case, we want to find the z-score that corresponds to a percentile of 95%, which is the same as 0.95.
3. Find the SAT score: Once you have determined the z-score corresponding to a percentile of 95%, you can use it to find the SAT score using the formula:
X = (z * σ) + μ
Plug in the value of the z-score, the mean (μ = 550), and the standard deviation (σ = 90) to calculate the SAT score at the 95th percentile.
I'll do the calculation for you:
1. Calculate the z-score:
z = (X - μ) / σ
z = (X - 550) / 90
2. Look up the z-score on a z-table or use a calculator that can compute z-scores and percentiles. For a percentile of 95%, the z-score is approximately 1.645.
3. Find the SAT score:
X = (z * σ) + μ
X = (1.645 * 90) + 550
X ≈ 694.05
Therefore, the SAT score at the 95th percentile is approximately 694.05. This means that 95% of the SAT scores fall below 694.05.