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Question
a digital thermometer reports a temperature of 62.6°f as being 61.58°f. which of the following is true?
a. the thermometer is precise, but not accurate.
b. the thermometer is both accurate and precise.
c. the thermometer is accurate, but not precise.
d. the thermometer is neither accurate nor precise.
To determine accuracy and precision:
- Accuracy: How close a measurement is to the true value. The true value here is \( 81.5^\circ\text{F} \), and the thermometer reports \( 82.4^\circ\text{F} \). The difference is small, so it is relatively accurate.
- Precision: How consistent (repeatable) measurements are. The thermometer reports a value with one decimal place, indicating a precise measurement (consistent in decimal places). However, the key is that the reported value is close to the true value (accurate) and the measurement has a precise decimal place. Wait, no—wait, the options: Let’s re-express. Wait, the true value is \( 81.5^\circ\text{F} \), and the thermometer says \( 82.4^\circ\text{F} \). Wait, maybe I misread. Wait, the problem says: “reports a temperature of \( 82.4^\circ\text{F} \) as being \( 81.5^\circ\text{F} \)”? Wait, no—wait, the text: “A digital thermometer reports a temperature of \( 82.4^\circ\text{F} \) as being \( 81.5^\circ\text{F} \).” Wait, no, maybe it’s a typo. Wait, no—probably, the thermometer measures a temperature (true value \( 81.5^\circ\text{F} \)) and reports \( 82.4^\circ\text{F} \). Wait, no, the problem is: “Which of the following is true?” Let’s analyze the options:
- Option A: Precise but not accurate. If it’s precise, measurements are consistent, but not close to true. But here, the reported value is close to true (so accurate), so A is wrong.
- Option B: Both accurate and precise. The reported value (\( 82.4^\circ\text{F} \)) is close to the true value (\( 81.5^\circ\text{F} \)) (accuracy), and the measurement has a decimal place (precision, as it’s consistent in reporting to one decimal). Wait, but maybe the thermometer’s measurement is accurate (close to true) and precise (consistent in decimal places). Wait, but let’s re-express:
Wait, maybe the problem is: The thermometer reports \( 82.4^\circ\text{F} \) when the true value is \( 81.5^\circ\text{F} \). Wait, no—maybe the true value is \( 81.5^\circ\text{F} \), and the thermometer says \( 82.4^\circ\text{F} \). The difference is \( 82.4 - 81.5 = 0.9^\circ\text{F} \), which is small, so accurate. The measurement is reported to one decimal place, so precise. Thus, the thermometer is both accurate (close to true) and precise (consistent in decimal places). Wait, but let’s check the options again. Wait, maybe I made a mistake. Wait, the options:
A. Precise, not accurate.
B. Both accurate and precise.
C. Accurate, not precise.
D. Neither.
Wait, if the thermometer reports a value with a decimal (precise) and the value is close to true (accurate), then B is correct. Wait, but maybe the problem is that the thermometer is reporting \( 82.4^\circ\text{F} \) as \( 81.5^\circ\text{F} \) (i.e., it’s misreporting). Wait, no—probably a typo. Let’s assume the true value is \( 81.5^\circ\text{F} \), and the thermometer measures \( 82.4^\circ\text{F} \). The accuracy: how close \( 82.4 \) is to \( 81.5 \) (difference \( 0.9 \), which is small, so accurate). Precision: the measurement has one decimal place, so it’s precise (consistent in decimal places). Thus, both accurate and precise. So option B.
Wait, but maybe I misread. Let’s re-express:
- Accuracy: Closeness to true value. \( 82.4 \) vs. \( 81.5 \): difference is \( 0.9^\circ\text{F} \), which is relatively accurate (not perfect, but close).
- Precision: The thermometer reports a value with one decimal place, so it’s precise (consistent in the number of decimal places, implying repeatable measurements).
Thus, the thermometer is both accurate (close to true) and prec…
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B. The thermometer is both accurate and precise.