Final answer:
The percentage of students who scored above a 390 on the SAT Mathematics test is 86.43%. This is calculated by finding the z-score for 390 and using it to determine the corresponding percentile on a standard normal distribution, which is then subtracted from 100%.
Step-by-step explanation:
To find the percentage of students who scored above a 390 on the SAT Mathematics test, given that the scores are normally distributed with a mean of 500 and a standard deviation of 100, we'll need to calculate the z-score for a score of 390 and then use a standard normal distribution table to find the corresponding percentile.
The z-score is calculated by taking the difference between the score and the mean, then dividing by the standard deviation:
z = (X - μ) / σ
Where X is the score, μ is the mean, and σ is the standard deviation. In this case:
z = (390 - 500) / 100 = -1.1
Looking at a standard normal distribution table, a z-score of -1.1 corresponds to a percentile of approximately 13.57%. This means that 13.57% of students scored below a 390. To find the percentage of students who scored above a 390, we subtract this number from 100%:
100% - 13.57% = 86.43%
Therefore, the correct answer is A) 86.43%.