Answer to Question #118636 in Statistics and Probability for Michael

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−Φ((90−73)/4)=1−Φ(4.25)=0

P₂={A₂>90}=1−Φ((90−73)/8)=1−Φ(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