Scores on the verbal section of the SAT have a mean of 500 and a standard deviation of 100. If someone scored at the 90th percentile, what is their SAT score?

Can someone show me how to find this equation to this problem?

Scores on the verbal section of the SAT have a mean of 500 and a standard deviation of 100. If someone scored at the 90th percentile, what is their SAT score?

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the Z score related to that proportion.

Z = (score-mean)/SD

Insert the values and solve for the score.

To find the SAT score corresponding to the 90th percentile, we can use the standard normal distribution table.

First, we need to convert the percentile to a z-score. The z-score represents the number of standard deviations above or below the mean a particular score is.

Since the 90th percentile is being considered, 10% of the scores will be above it (100 - 90 = 10). Therefore, we want to find the z-score for the 90th percentile.

Looking at the standard normal distribution table, the closest z-score to 10% is approximately 1.28.

Next, we can use the formula:

z = (x - mean) / standard deviation

Rearranging the formula to solve for x (SAT score), we have:

x = (z * standard deviation) + mean

Substituting the values we have:

x = (1.28 * 100) + 500

x = 128 + 500

x = 628

Therefore, a score of 628 on the verbal section of the SAT corresponds to the 90th percentile.

To find the SAT score of someone who scored at the 90th percentile, you can use the concept of z-scores and the standard normal distribution table.

1. Convert the percentile to a z-score: The z-score represents the number of standard deviations the score is from the mean. To find the z-score, you can use the formula: z = (x - mean) / standard deviation. In this case, the percentile is 90, so the z-score can be found by using the formula: z = invNorm(0.90).

2. Once you have the z-score, you can convert it back to the corresponding SAT score by using the formula: x = z * standard deviation + mean. In this case, the mean is 500 and the standard deviation is 100, so the SAT score can be found by calculating: x = z * 100 + 500.

Let's calculate the SAT score using these steps:

1. Find the z-score: Using the invNorm function in a statistical calculator or a normal distribution table, you can find that invNorm(0.90) is approximately 1.28.

2. Calculate the SAT score: Using the formula x = z * standard deviation + mean, plug in the values: x = 1.28 * 100 + 500.

x = 128 + 500 = 628.

Therefore, a person who scored at the 90th percentile on the verbal section of the SAT would have a score of 628.