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 measurements demonstrate higher precision than student b but not accuracy. student c has the least accurate measurement. student c has the most accurate measurement. none of the above

Explanation:

Step1: Define precision and accuracy

Precision is closeness of repeated measurements. Accuracy is closeness to true - value.

Step2: Analyze Student B's precision

Student B's measurements: 86.9 mL, 87.1 mL, 87.2 mL. The values are very close to each other.

Step3: Analyze Student C's precision

Student C's measurements: 87.6 mL, 87.8 mL, 87.9 mL. The values are also close but more spread out than B's. So B has higher precision than C.

Step4: Analyze Student A's precision and accuracy

Student A's measurements: 87.1 mL, 88.2 mL, 87.6 mL. The values are more spread out than B's, so A has lower precision than B. Also, the values are not very close to 87.0 mL, so not accurate.

Step5: Analyze Student C's accuracy

The average of Student C's measurements: $\frac{87.6 + 87.8+87.9}{3}=\frac{263.3}{3}\approx87.77$ mL. The average of Student A's measurements: $\frac{87.1 + 88.2+87.6}{3}=\frac{262.9}{3}\approx87.63$ mL. The average of Student B's measurements: $\frac{86.9 + 87.1+87.2}{3}=\frac{261.2}{3}\approx87.07$ mL. Student C's average is further from 87.0 mL compared to B, so C has less accurate measurement.

Answer:

Student B's measurements demonstrate higher precision than Student C.
Student C has the least accurate measurement.