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.
Which portion of the bell curve relates to the answer?
What is the % scored?
what % of the persons who take the test score above 1300?
What % score above 800?
What % score below 1,200?
Above what score do 20% of the test-takers score?
Above what score do 30% of the test-takers score?
To answer these questions, we can use the properties of the normal distribution, also known as the bell curve. Here's how you can find the answers step by step:
1. Which portion of the bell curve relates to the answer?
In this case, since the scores on the GRE follow a normal distribution, the entire bell curve relates to the answer. Any specific portion of the curve depends on the specific score range mentioned in the question.
2. What is the % scored?
To find the percentage scored within a specific range, we need to use the z-score formula. The z-score represents the number of standard deviations a particular score is above or below the mean.
The z-score formula is:
z = (X - μ) / σ
where X is the score, μ is the mean, and σ is the standard deviation.
For example, to find the percentage of scores below 1,200, we can calculate the z-score as follows:
z = (1200 - 1000) / 200 = 1
To find the percentage corresponding to a z-score, we can use a standard normal distribution table or calculator. Looking up the z-score of 1 in the table, we find that it corresponds to approximately 84.13%.
Therefore, approximately 84.13% of test-takers score below 1,200.
3. What % of the persons who take the test score above 1300?
Similarly, we can calculate the z-score for a score of 1300:
z = (1300 - 1000) / 200 = 1.5
Using the standard normal distribution table, we find that a z-score of 1.5 corresponds to approximately 93.32%.
Therefore, approximately 6.68% of test-takers score above 1300.
4. What % score above 800?
Following the same process, we can calculate the z-score for a score of 800:
z = (800 - 1000) / 200 = -1
Using the standard normal distribution table, we find that a z-score of -1 corresponds to approximately 15.87%.
Therefore, approximately 84.13% of test-takers score above 800.
5. What % score below 1,200?
As discussed earlier, the percentage of test-takers who score below 1,200 is approximately 84.13%.
6. Above what score do 20% of the test-takers score?
To find the score above which 20% of test-takers score, we use the inverse z-score formula. In other words, we find the z-score that corresponds to the desired percentage.
Using the inverse z-score formula, we can calculate this as follows:
z = invNorm(1 - 0.20) = invNorm(0.80)
Using a standard normal distribution table or calculator, we find that the z-score corresponding to 0.80 is approximately 0.84.
Now, we can calculate the score using the z-score formula:
X = (z * σ) + μ
X = (0.84 * 200) + 1000 = 1168
Therefore, approximately 20% of test-takers score above 1,168.
7. Above what score do 30% of the test-takers score?
Following the same process as before, we find the inverse z-score for 30%:
z = invNorm(1 - 0.30) = invNorm(0.70)
Using a standard normal distribution table or calculator, we find that the z-score corresponding to 0.70 is approximately 0.52.
Calculating the score:
X = (z * σ) + μ
X = (0.52 * 200) + 1000 = 1104
Therefore, approximately 30% of test-takers score above 1,104.