Given that math SAT scores are normally distributed (follow the empirical rule)

m=500 Standard deviation=100

what is the math SAT score for someone who is in the 80th percentile of his or her class.

To find the math SAT score for someone who is in the 80th percentile, we need to understand the concept of percentile and how it relates to the standard deviation and mean of a normal distribution.

The 80th percentile indicates that 80% of the individuals in the class scored below a certain score. To find this score, we can make use of z-scores, which measure the number of standard deviations a particular value is away from the mean.

According to the empirical rule of a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

In this case, we can see that the mean (m) is 500 and the standard deviation (σ) is 100. So, to determine the z-score corresponding to the 80th percentile, we need to find the value of z that gives us an area of 0.80 to the left of it.

Using a z-table or a statistical calculator, we find that the z-score associated with the 80th percentile is 0.84.

To find the math SAT score for someone in the 80th percentile, we can use the formula:

x = m + (z * σ)

Substituting the values we have:

x = 500 + (0.84 * 100)
x = 500 + 84
x = 584

Therefore, the math SAT score for someone who is in the 80th percentile of their class is 584.