Question

three students (a, b, and c) are asked to determine the volume of a sample of ethanol. each student measures the volume three times with a graduated cylinder. the results are: a: 87.1 ml, 88.2 ml, 87.6 ml b: 86.9 ml, 87.1 ml, 87.2 ml c: 87.6 ml, 87.8 ml, 87.9 ml the true volume is 87.0 ml. which of the following statements is/are true about the three students measurements? check all that apply. student bs measurements demonstrate higher precision than student c. student as results are more accurate than student b. student as measurements demonstrate higher precision than student b but not accuracy. student as measurements demonstrate higher accuracy than student c but not student b. none of the above

Explanation:

Step1: Define accuracy and precision

Accuracy is closeness to true - value. Precision is closeness of measurements to each other.

Step2: Analyze Student A's measurements

Student A: 87.1 mL, 88.2 mL, 87.6 mL. Values are spread out, not very precise. Average is $\frac{87.1 + 88.2+87.6}{3}=\frac{262.9}{3}\approx87.63$ mL.

Step3: Analyze Student B's measurements

Student B: 86.9 mL, 87.1 mL, 87.2 mL. Values are close to each other (precise) and close to 87.0 mL (accurate). Average is $\frac{86.9 + 87.1+87.2}{3}=\frac{261.2}{3}\approx87.07$ mL.

Step4: Analyze Student C's measurements

Student C: 87.6 mL, 87.8 mL, 87.9 mL. Values are close to each other (precise) but higher than 87.0 mL (less accurate). Average is $\frac{87.6 + 87.8+87.9}{3}=\frac{263.3}{3}\approx87.77$ mL.

Step5: Evaluate statements

• Student B's values are closer to each other than Student C's in terms of range. So, Student B's measurements demonstrate higher precision than Student C.
• Student B's average is closer to 87.0 mL than Student A's. So, Student A's results are not more accurate than Student B.
• Student A's measurements are less precise than Student B's.
• Student A's average is not closer to 87.0 mL than Student C's or Student B's.

Answer:

Student B's measurements demonstrate higher precision than Student C.