the verbal section of GRE exam for admission into graduate school has a mean of 456 (s=140). Assuming the scores are normally distributed what percent of students will score 600 or higher? (choose range that fits your answer)
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score. Multiply by 100.
To determine the percentage of students who will score 600 or higher on the verbal section of the GRE exam, we need to calculate the z-score and then find the corresponding percentile.
The formula for calculating the z-score is:
z = (x - μ) / σ
Where:
- x is the raw score (600 in this case),
- μ is the mean of the distribution (456 in this case), and
- σ is the standard deviation of the distribution (140 in this case).
Substituting the values into the formula:
z = (600 - 456) / 140
z = 144 / 140
z ≈ 1.03
Now, we need to find the percentile associated with this z-score. We can use a standard normal distribution table or a calculator to find this value. Let's assume we use a standard normal distribution table.
Looking up the z-score of 1.03 in the table, we find that the corresponding percentile is approximately 84%. This means that about 84% of students will score 600 or below on the verbal section of the GRE exam.
Therefore, the percentage of students that will score 600 or higher is (100% - 84%) = 16%.