The probability that Anna obtains the highest grade among the three students can be determined by calculating the probability that Anna scores higher than both Sandra and Jessy. Because the scores are roughly normally distributed with a mean of 527 and a standard deviation of 90, we can use the standard normal distribution to calculate the probability.
First, we need to convert Anna's score to a standard score by subtracting the mean and dividing by the standard deviation. Let's say Anna scored a 580 on the GMAT. The standard score is then (580 - 527) / 90 = 0.7.
Then, we need to find the probability that Anna's score is higher than both Sandra's and Jessy's scores. Because the scores are independent, we can simply multiply the probabilities that Anna's score is higher than each of Sandra's and Jessy's scores.
To find the probability that Anna's score is higher than Sandra's score, we need to find the area under the standard normal curve to the right of Anna's standard score. Using a standard normal table or a calculator, we can find that this probability is 0.7448.
To find the probability that Anna's score is higher than Jessy's score, we again need to find the area under the standard normal curve to the right of Anna's standard score. This probability is also 0.7448.
The probability that Anna obtains the highest grade is then 0.7448 * 0.7448 = 0.5534, or about 55.34%. This means there is about a 55.34% chance that Anna will obtain the highest grade among the three students.