The Graduate Record Exam (GRE) has a combined verbal and quantitative mean of 1000 and a standard deviation of 200. Scores range from 200 to 1600 and are approximately normally distributed. What percentage score above 1300? What percentage score above 800? What percentage score below 1200? Above what score do 20% score? Above what score do 20% score?

How do I calculate percentages with SD and mean?

http://davidmlane.com/hyperstat/z_table.html

To calculate percentages using the mean and standard deviation, you can utilize the concept of standardized scores, also known as z-scores.

A z-score measures how many standard deviations a particular value is from the mean. It can be calculated using the formula:

z = (x - μ) / σ

Where:
- z is the z-score
- x is the individual score
- μ is the mean
- σ is the standard deviation

Once you have the z-score, you can use a standard normal distribution table or a calculator to find the corresponding percentage.

Now, let's answer the specific questions using this approach:

1. What percentage score above 1300?
First, calculate the z-score:
z = (1300 - 1000) / 200 = 1.5

Using a standard normal distribution table, the area to the right of 1.50 (above 1.50) is approximately 0.4332. This means that about 43.32% of the scores are above 1300.

2. What percentage score above 800?
Calculate the z-score:
z = (800 - 1000) / 200 = -1.0

Using the standard normal distribution table, the area to the right of -1.00 (above -1.00) is approximately 0.8413. We need to subtract this value from 1 to get the area above 800, which is approximately 1 - 0.8413 = 0.1587. Therefore, about 15.87% of the scores are above 800.

3. What percentage score below 1200?
Calculate the z-score:
z = (1200 - 1000) / 200 = 1.0

Using the standard normal distribution table, the area to the left of 1.00 (below 1.00) is approximately 0.8413. This means that about 84.13% of the scores are below 1200.

4. Above what score do 20% score?
To find the score above which 20% of the scores lie, you need to find the z-score that corresponds to an area of 0.80 (1 - 0.20) in the standard normal distribution table. In this case, use the inverse of the z-score formula:

z = invNorm(0.80) = 0.84 (approximately)

Now, solve for x:
0.84 = (x - 1000) / 200

Rearranging the equation:
x - 1000 = 0.84 * 200
x - 1000 = 168
x = 1168

Therefore, a score of approximately 1168 or above is needed for 20% of the scores.

It's important to note that the percentages provided are approximations since the standardized normal distribution table gives only a limited number of precise values.