Final answer:
The statement is false because all but one student have a mean grade between 79 and 82.
Step-by-step explanation:
The statement is b. False.
The mean grade of the class is given as 80. We are told that 19 students have a mean grade between 79 and 82, inclusive. This means that only one student can have a grade that is outside this range. Since the mean grade is 80, the only way for the statement to be true is if this one student has a grade below 79 or above 82, which is not the case. Therefore, the statement is false.
The mean grade for these 19 can fluctuate slightly while still keeping the class mean at 80, as the 20th student's score, which is not provided, could be higher or lower and still result in an average of 80 for the entire class.
This scenario is akin to the ones in Example 6.8 and Example 2.21 provided in the reference where a set of scores have a known mean and students' individual scores are measured in relation to this mean and the potential standard deviation.