Question

In a data set of 200 observations with a rage of 63.5 to 102.3, there are 138 observations with values less than 89.2 ,

Answer 1

"find the percentile" means: "what percentage of the data points is below a certain value".

Here it's 138 data points out of 200, which is:

$\frac{138}{200} = \frac{69}{100}*100% =69$.

The answer is 69, and we phrase it as "the 69th percentile of data is at the value of 89.2"

You actually don't need to know the range to solve this!