In order to make an entry to a certain university, it is required to pass a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. Aswin wants to be admitted to this university and he knows that he must score better than at least 70% of the students who took the test. Aswin takes the test and scores 585. Will he be admitted to this university?
High-Yield Explanation
For X = 585, Z = (585 – 500) / 100 = 0.85
The proportion P of students who scored below 585 is given by
P = = 0.8023 = 80.23%
Aswin scored better than 80.23% of the students who took the test and he will be admitted to this university.