Solved – How to find a percentile with the mean and standard deviation only

The scores on a nationwide math exam are normally distributed with a mean = 80, SD = 12. Find the raw score that divides the distribution of aptitude scores such that 70% of the scores are below it.

I assume this is a homework question, so I'll give you the tools but not the answer. First you need the cumulative density function (CDF) of the distribution. This is a function that produces the area under the curve to the left of the input value. The area under the curve is the proportion of scores less than the given value. You want to get the value from the proportion (i.e., percentile), so you need the inverse CDF, which produces the value for which the given proportion of scores (e.g., 70%) is less than it. The inverse CDF can be found in statistical software, but you can also use a Z-table (below).

enter image description here

Find the value of Z for which .7 of the area under the curve is to the left. From the Z-score, use the Z-score formula and the given mean and SD to solve for the raw score.

Similar Posts:

Rate this post

Leave a Comment