"A curious student in a large economics course is interested in calculating the percentage of his classmates who scored lower than he did on the GMAT; he scored 490. He knows that GMAT scores are normally distributed and that the average score is approximately 540. He also knows that 95% of his classmates scored between 400 and 680. Based on this information, calculate the percentage of his classmates who scored lower than he did."

 23.89%

Step-by-step explanation:

The empirical rule says that the 95% of the data falls in between two standard deviations of the mean.

Given : GMAT scores are normally distributed and the the average score is approximately .

Also, 95% of his classmates scored between 400 and 680.

Then, by empirical rule , 95% of data falls in between

i.e.    (1)

      (2)

Subtracting (1) from (2), we get

Let x be the random variable to represent the scores of every student.

Statistic z-score :

For x= 490, we have

The p-value =

Hence, 23.89% of his classmates who scored lower than he did .