How do I find a percentile if I only have the mean and sd? ie...what IQ score is associated with the 65th percentile?-mean is 100 and sd is 15. Thanks in advance :)

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion (.65) related to the Z score. Insert the values into the equation above and solve for the IQ.

To find the IQ score associated with a specific percentile using the mean and standard deviation, you can use the Z-score formula. The Z-score measures how many standard deviations an individual score is from the mean.

Here's how you can find the IQ score associated with the 65th percentile:

Step 1: Convert the percentile to a Z-score
To convert the percentile to a Z-score, you can use the standard normal distribution table or a Z-score calculator. The formula is:
Z = (X - μ) / σ

Where:
Z is the Z-score
X is the raw score (IQ score in this case)
μ is the mean
σ is the standard deviation

Substituting the values you provided:
Z = (X - 100) / 15

Step 2: Find the Z-score associated with the percentile
To find the Z-score associated with the 65th percentile, you need to look up the area in the standard normal distribution table. The table will provide the Z-score that corresponds to the desired percentile. In this case, you're looking for the Z-score that corresponds to 0.65.

Step 3: Solve for the IQ score
Once you have the Z-score corresponding to the percentile, you can rearrange the formula from Step 1 to solve for X (the IQ score):
X = Z * σ + μ

Substituting the values you provided:
X = Z * 15 + 100

Using this method, you can find the IQ score associated with any percentile given the mean and standard deviation. In this case, you wanted to find the IQ score associated with the 65th percentile.