Final answer:
The length of time needed to complete the test is normally distributed with a mean of 60 minutes and a standard deviation of 10 minutes. 99.7% of the students will finish the test between 30 and 90 minutes.
Step-by-step explanation:
The length of time needed to complete a certain test is normally distributed with a mean of 60 minutes and a standard deviation of 10 minutes. To find the time interval within which 99.7% of the students will finish, we can use the empirical rule. The rule states that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations of the mean.
Since the mean is 60 minutes and the standard deviation is 10 minutes, we can calculate three standard deviations above and below the mean. Three standard deviations below the mean is 60 - 3(10) = 30 minutes. Three standard deviations above the mean is 60 + 3(10) = 90 minutes. Therefore, 99.7% of the students will finish the test between 30 and 90 minutes, which corresponds to answer choice A) Between 30 and 90 minutes.