Final answer:
To find the percentage of students with GMAT scores between 400 and 800, we calculate the z-scores for both scores and find the area under the normal distribution curve between those z-scores. The percentage is approximately 95.45%.
Step-by-step explanation:
To find the percentage of students with GMAT scores between 400 and 800, we need to calculate the z-scores for both scores and then find the area under the normal distribution curve between those z-scores.
The formula for calculating the z-score is (x - μ) / σ, where x is the individual score, μ is the mean, and σ is the standard deviation.
For a score of 400, the z-score is (400 - 600) / 100 = -2.00. For a score of 800, the z-score is (800 - 600) / 100 = 2.00. Looking up these z-scores in a standard normal distribution table, we find that the area between -2.00 and 2.00 is approximately 0.9545.
Therefore, approximately 95.45% of students have GMAT scores between 400 and 800.