Question

use the body temperatures, in degrees fahrenheit, listed in the accompanying table. the range of the data is 3.8°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, 0.74°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 0.95°f
(round to two decimal places as needed.)
compare the result to the actual standard deviation.
the estimated standard deviation is more than 0.2° greater than the actual standard deviation. thus, the estimated standard deviation dropdown options: meets, does not meet the goal

Explanation:

Step1: Recall range - rule - of - thumb

The range - rule of thumb for estimating the standard deviation is $s\approx\frac{R}{4}$, where $R$ is the range. Given $R = 3.8^{\circ}F$, then $s\approx\frac{3.8}{4}=0.95^{\circ}F$.

Step2: Compare with actual standard deviation

The actual standard deviation is $0.74^{\circ}F$. The difference between the estimated and actual standard deviation is $0.95 - 0.74=0.21^{\circ}F$. Since $0.21>0.2$, the estimated standard deviation is more than $0.2^{\circ}$ greater than the actual standard deviation.

Answer:

does not meet