For a set of scores with a mean of 111 and a standard deviation of 8, what is the percentile rank of 90? (round to two decimal places, no leading zeros)
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (.90) and its Z score. Insert in equation above and solve for score.
To find the percentile rank of a score, you can use the normal distribution table or a statistical calculator. Here's how you can calculate it using the Z-score formula:
1. Calculate the Z-score of the score you want to find the percentile rank for.
Z = (X - μ) / σ
Where:
Z = Z-score
X = Score
μ = Mean
σ = Standard deviation
In this case:
X = 90
μ = 111
σ = 8
Z = (90 - 111) / 8
Z = -2.625
2. Look up the Z-score in the normal distribution table or use a statistical calculator to find the area under the curve to the left of that Z-score.
Using the table or a calculator, you can find that the area to the left of Z = -2.625 is approximately 0.00447.
3. Calculate the percentile rank.
Percentile Rank = (Area to the left of Z) x 100
Percentile Rank = 0.00447 x 100
Percentile Rank = 0.447
Therefore, the percentile rank of 90 in a set of scores with a mean of 111 and a standard deviation of 8 is approximately 0.447 or 0.45 (rounded to two decimal places).