# Percentile rank

#### kate

##### New Member
Can someone help me with the following problem? Thanks in advance !

Jon Molnar will graduate from Carolina Forest High School this
year. He took the American College Test (ACT) for college admission and
received a score of 30. The high school principal informed him that
only 2 percent of the students taking the exam receive a higher score.
The mean score for all students taking the exam is 18.3. Jon s friends
Karrie and George also took the test but were not given any information
by the principal other than their scores. Karrie scored 25 and George
18. Based on this information, what were Karrie s and George s
percentile ranks?
Assume that the distribution of scores follows the normal distribution.

#### quark

Hi Kate,

Welcome to TalkStats.

Since Jon is at the 98th percentile,

P(Z<2.06)=0.98

We solve for sd using the z-score of 2.06.

(X-mean)/sd = 2.06
(30-18.3)/sd = 2.06
sd=5.68

Kerrie's z-score is given by:

(25-18.3)/5.68=1.18

P(Z<1.18)=0.8810

Kerrie is at the 88.1 percentile.

You should be able to figure out George's percentile rank. Please post here if you have further questions.

Cheers,

quark