The GRE has a combined verbal and quantitative mean of 1000 and standard deviation of 200. Scores range from 200 to 1600.
a. what % of the persons score above 1300?
b. above 800?
c. below 1200?
d. above what score do the top 20% of the test-takers score?
e. Below what score do the bottom 16% of the test-takers score?
you can play around with Z table stuff at
http://davidmlane.com/hyperstat/z_table.html
To solve these questions, we'll use the properties of the normal distribution and the z-score formula. The z-score formula is given by:
z = (x - μ) / σ
where:
z is the z-score,
x is the raw score,
μ is the mean, and
σ is the standard deviation.
Now let's solve each question step by step:
a. What % of the person's score above 1300?
To answer this question, we need to find the area to the right of 1300 under the normal distribution curve.
First, we calculate the z-score for 1300:
z = (1300 - 1000) / 200 = 3
Next, we find the area to the right of this z-score using a standard normal distribution table or a calculator. Looking up the z-score of 3 in the table, we find that the area to the right is approximately 0.0013.
So, about 0.13% of the person's score is above 1300.
b. What % of the persons score above 800?
Similarly, we calculate the z-score for 800:
z = (800 - 1000) / 200 = -1
Now we find the area to the right of this z-score. Looking up the z-score of -1 in the table, we find that the area to the right is approximately 0.8413.
So, about 84.13% of the person's score is above 800.
c. What % of the persons score is below 1200?
To find the area below 1200, we use the same z-score formula:
z = (1200 - 1000) / 200 = 1
Now we find the area to the left of this z-score. Looking up the z-score of 1 in the table, we find that the area to the left is approximately 0.8413.
So, about 84.13% of the person's score is below 1200.
d. Above what score do the top 20% of the test-takers score?
To answer this question, we need to find the z-score that corresponds to the top 20% of the distribution.
Using the standard normal distribution table, we find that the z-score corresponding to the top 20% is approximately 0.8416.
Now we can calculate the raw score (x) using the z-score formula:
0.8416 = (x - 1000) / 200
Solving for x, we get:
x = (0.8416 * 200) + 1000 = 168.32 + 1000 = 1168.32
So, the top 20% of test-takers score above approximately 1168.32.
e. Below what score do the bottom 16% of the test-takers score?
Similarly, we find the z-score corresponding to the bottom 16% using the standard normal distribution table. The z-score is approximately -0.9945.
Now we calculate the raw score (x) using the z-score formula:
-0.9945 = (x - 1000) / 200
Solving for x, we get:
x = (-0.9945 * 200) + 1000 = -198.9 + 1000 = 801.1
So, the bottom 16% of test-takers score below approximately 801.1.