Question

use the body temperatures, in degrees fahrenheit, listed in the accompanying table. the range of the data is 3.1°f. use the range - rule of thumb to estimate the value of the standard - deviation. compare the result to the actual standard deviation of the data rounded to two decimal places, 0.66°f, assuming the goal is to approximate the standard deviation within 0.2°f. click the icon to view the table of body temperatures. the estimated standard deviation is □°f (round to two decimal places as needed.) compare the result to the actual standard deviation. the estimated standard deviation is the actual standard deviation. thus, the estimated standard deviation the goal.

Explanation:

Step1: Apply range - rule of thumb

The range - rule of thumb states that the standard deviation $s\approx\frac{\text{Range}}{4}$. Given that the range of the data is $3.1^{\circ}F$. So, $s\approx\frac{3.1}{4}$.

Step2: Calculate the estimated standard deviation

$\frac{3.1}{4}= 0.78^{\circ}F$ (rounded to two decimal places).

Step3: Compare with actual standard deviation

The actual standard deviation is $0.66^{\circ}F$. The difference between the estimated and actual standard deviation is $|0.78 - 0.66|=0.12^{\circ}F$. Since $0.12^{\circ}F<0.2^{\circ}F$, the estimated standard deviation is within $0.2^{\circ}F$ of the actual standard deviation.

Answer:

The estimated standard deviation is $0.78^{\circ}F$.
The estimated standard deviation is within $0.2^{\circ}F$ of the actual standard deviation. Thus, the estimated standard deviation meets the goal.