Final answer:
The correct interpretation of the standard deviation is that it tells us how much a student's grade typically varies from the mean. Option A is correct if the standard deviation is 1.16, while Option B would be correct if the standard deviation is actually 1.08.
Step-by-step explanation:
The statement that correctly interprets the standard deviation of the grade distribution would be the one that reflects how much the grades vary from the mean, on average. The standard deviation is a measure of the dispersion of a set of data from its mean. If a random value is chosen from the dataset, in this case, a student's grade, the standard deviation will tell us, on average, how much that student's grade is expected to differ from the mean grade.
Given the choices provided, the correct interpretation of the standard deviation in relation to a student's grade would be 'A. The grade for a randomly selected student would typically vary from the expected grade by 1.16' if the standard deviation is indeed 1.16.
'B. The grade for a randomly selected student would typically vary from the expected grade by 1.08' would be the correct choice if the actual standard deviation were 1.08. However, without the specific value, we cannot confirm this statement.