# z-score

• Oct 28th 2010, 09:23 AM
terminator
z-score
the average mark on a set of university entrance exams was 70% with a standard dev. of 9.6. In order to be accepted into university, a student had to achieve a mark of 60% of better. If 800 students wrote the exam, approximately how many were accepted?
480
560
680
760

z-score = 800 - 60??/9.6
What am I doing wrong?
• Oct 28th 2010, 10:15 AM
Unknown008
You are using your z formula wrongly.

$z = \dfrac{x - \mu}{\sigma}$

What is the value of x, the percentage that you are looking for?
What is the value of mu, the mean/average percentage that was given?

Form that, you get the z score and the probability that any student gets above 60%.

That's for 1 student. What is the expectation with 800 students? (Hint: Expectation = np)
• Oct 28th 2010, 04:37 PM
terminator
OK. z= 60-70/9.6 = -1.04 the probability is 0.1492
800 x 0.1492 = 119.36

"In mathematics, you don't understand things. You just get used to them." -- Johann von Neumann
• Oct 28th 2010, 08:24 PM
mr fantastic
Quote:

Originally Posted by terminator
OK. z= 60-70/9.6 = -1.04 the probability is 0.1492 Mr F says: This probability is clearly wrong. If the mean is 70 then the probability of being less than 70 is clearly going to be greater than 0.5 .... You have made simple mistake. Go back and check.

800 x 0.1492 = 119.36

"In mathematics, you don't understand things. You just get used to them." -- Johann von Neumann

..
• Oct 28th 2010, 10:12 PM
Unknown008
The probability that you got is the probability of a student of getting less than 60%, that is the probability that they were not accepted. To help you, always make a sketch of the normal distribtution and shade the area that you are required to find. You table gives values to the left of the z score while you are looking for the probability to the right of the z score.

Try again.
• Oct 29th 2010, 04:30 AM
terminator