To determine if a grade of 70 falls within the acceptable range for a grade of C, we need to consider the average grade and the amount of acceptable variance.
1. Given Information:
- The average grade in the class is 74.5.
- A grade of C can vary by 5 points in either direction.
2. Calculating the Acceptable Range for a Grade of C:
- To find the lower bound of the range, subtract the variance (5 points) from the average grade:
[tex]\[
\text{Lower Bound} = 74.5 - 5 = 69.5
\][/tex]
- To find the upper bound of the range, add the variance (5 points) to the average grade:
[tex]\[
\text{Upper Bound} = 74.5 + 5 = 79.5
\][/tex]
3. Determining if a Grade of 70 Falls within the Range:
- The acceptable range for a grade of C is from 69.5 to 79.5.
- Check if a grade of 70 falls between 69.5 and 79.5:
[tex]\[
69.5 \leq 70 \leq 79.5
\][/tex]
- Since 70 is within this range, it falls within the acceptable range for a grade of C.
Thus, the correct answer is:
- Yes, because the range is 69.5 to 79.5 for a C at this school.
