Question

Two teachers have classes of similar sizes. After the final exams, the mean of the grades in each class is 73%. However, one class has a standard deviation of 4% while the other is 8%. In which class would a mark of 90% be more meaningful?

Answer 1

the distribution in both classes can be taken as Normal distribution.

A₁ first class, A₂ second class.

A₁=N(73,4), A₂=N(73,8)

P₁={A₁>90}= $1-\Phi((90-73)/4)=1-\Phi(4.25)=0$

$\Phi(3,5)=1$

P₂={A₂>90}=$1-\Phi((90-73)/8)=1-\Phi(2.125)=1-0.9834=0.0166$

this means that in the second grade, there was a probability of about 2% of students with a score of more than 90%, when in the first there are no such students at all

in the second grade a score of 90% is more likely

the reference to a calculation formula and a data table

(https://en.wikipedia.org/wiki/Normal_distribution,https://www.normaltable.com)