Final answer:
Using the empirical rule, we find that 34% of students should have scored between 20 and 40 on the test. After calculating 34% of 10,000, we get 3,400 students. The closest answer given the provided options is 3,334 students, acknowledging some deviation from a perfect normal distribution or rounding in the answer choices.
Step-by-step explanation:
The question involves applying the empirical rule (or 68-95-99.7 rule), which applies to normally distributed datasets. A score between 20 and 40 on a test with a mean of 40 and a standard deviation of 10 includes all the scores from one standard deviation below the mean to the mean itself. According to the empirical rule, 34% of the data lies between the mean and one standard deviation below the mean in a normal distribution. Therefore, we can calculate the number of students who scored between 20 and 40 by taking 34% of the total number of students who took the test.
To calculate the number of students: 34% of 10,000 students = 0.34 × 10,000 = 3,400 students.
However, the provided options do not include 3,400. Considering the nature of the empirical rule, which is approximate, the closest answer to our calculation is option b. 3,334, which most likely results from the test not perfectly adhering to a normal distribution or from rounding in the options provided.