You are Here: Home >< Maths

1. On a test by 100 students, the average mark is 65, with variance 144. student A scores 83, student B scores 47
a) calculate the z-scores for these two students
b) what is the maximum number of students with a score either better than A's or worse than B's
c) what is the maximum number of students with a score better than A's? (using chebyshev's inequality theory)

Can anyone help me on this ? desparately. Rest assured rep will be awarded.
2. z-scores? Is that the normal distribution?
3. I guess you could assume test scores to be in a normal distribution.
4. yes normal distribution
5. (Original post by iceman_jondoe)
On a test by 100 students, the average mark is 65, with variance 144. student A scores 83, student B scores 47
a) calculate the z-scores for these two students
Assuming the marks are distributed normally then, let X be the DRV 'marks obtained in test' then,

X ~ N(65, 12²)
P(X » 83) = (83-65)/12 = 1.5
P(X « 47) = (47-65)/12 = -1.5
6. (Original post by iceman_jondoe)
On a test by 100 students, the average mark is 65, with variance 144. student A scores 83, student B scores 47
b) what is the maximum number of students with a score either better than A's or worse than B's
b)P(X>83) = P(Z>[83-65]/12)
= P(Z>1.5)
= 1 - 0.9332
= 0.0668
p(X<47) = P(Z<[47-65]/12)
= P(Z<-1.5)
= 0.0668
P(score either better than A's or worse than B's)
= 0.0668 + 0.0668
=0.1336

Therefore, the maximum number of students with a score either better than A's or worse than B's
= 0.1336 . 100 (Since there are 100 students)
= 13.36
= 13 students

Is it right or wrong? And sorry I've never heard of chebyshev's inequality theory. But I just do it in this way...

c)the maximum number of students with a score better than A's
= 0.0668 . 100
= 6.68
= 7 students

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: January 28, 2006
Today on TSR

### University open days

• University of Roehampton
Sat, 17 Nov '18
• Edge Hill University
Faculty of Health and Social Care Undergraduate
Sat, 17 Nov '18
• Bournemouth University
Sat, 17 Nov '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams