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 in the 80th percentile, you need to convert the percentile to a z-score and then use the z-score to find the corresponding value on the normal distribution.

Step 1: Convert percentile to a z-score
The 80th percentile can be thought of as the value below which 80% of the data falls. To convert this percentile to a z-score, you can use the z-score formula: z = (x - m) / σ, where x is the value, m is the mean, and σ is the standard deviation.

z = (x - 500) / 100

Step 2: Find the z-score corresponding to the 80th percentile
To find the z-score that corresponds to the 80th percentile, you need to find the z-value in the cumulative standard normal distribution table that corresponds to a cumulative probability of 0.80. This can be done by looking up the value in the table or by using a calculator or statistical software.

From the standard normal distribution table or calculator, you will find that the z-score corresponding to a cumulative probability of 0.80 is approximately 0.84.

Step 3: Solve for x (math SAT score)
Now that you have the z-score, you can solve the z-score formula for x to find the math SAT score.

0.84 = (x - 500) / 100

Simplify and solve for x:

0.84 * 100 = x - 500

84 = x - 500

x = 84 + 500

x = 584

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