Question

4. After a general culture test, it was observed that the scores obtained followed an N(65, 18) distribution. We want to classify those examined into three groups (low general culture, acceptable general culture, excellent general culture) so that in the first group there are 20% of the population, 65% in the second and 15% in the third. What should the scores be that mark the passage from one group to the other?

Answer 1

Let X denote the score. then

The lower 20% fall in the low general culture.

Let 'a' be such that

The upper 150% fall in the excellent general culture.

Let 'b' be such that

Thus, the score 49.8512 marks the passage from 1st group to 2nd group and the score 83.6552 marks the passage from 2nd group to 3rd group.