# Word Problem involving Percentiles?

#### tdotodot

I'm doing exam review and am having trouble with this. Can someone please help explain it to me?

This is one of the questions:

Scores on a Test are worth 40 marks.

a) If a student scores at the 80th percentile, what is the students raw score?

b) In which percentile are the students who scored 30/40?

c) If a student scores in the 70th percentile, what did they get on the test?

#### chiro

MHF Helper
Hey tdotodot.

To answer this you need to have a distribution of marks. Do you want to assume that they are uniformly distributed from 0 to 40 (discrete uniform that is)?

#### tdotodot

Hey tdotodot.

To answer this you need to have a distribution of marks. Do you want to assume that they are uniformly distributed from 0 to 40 (discrete uniform that is)?
The question does not specify. However I believe that is the correct way.

#### chiro

MHF Helper
One reason I ask is that typically marks have more of a Normal distribution or a skewed distribution.

However if its uniform between a and b (whole numbers only and both inclusive) then the percentile score in percent for an observation x is p(x) = (x-a)/[b-a] * 100% where x lies in the interval of whole numbers [a,b]