Question

The brain volumes ​(cm cubedcm3​) of 50 brains vary from a low of 922922 cm cubedcm3 to a high of 14961496 cm cubedcm3. use the range rule of thumb to estimate the standard deviation s and compare the result to the exact standard deviation of 161.7161.7 cm cubedcm3​, assuming the estimate is accurate if it is within 15 cm cubedcm3.

Answer 1

The range rule of thumb is that the range is four times the standard deviation. The range in this case is 922 cubic cm to 1496 cubic cm, i.e., 574 cubic cm.
Therefore, according to the rule, the standard deviation is 574 cubic cm/4 = 
143.5 cubic cm. The actual standard deviation is 161.7 cubic cm. The difference is 161.7 - 143.5 = 18.2. Since this is greater than 15 cubic cm, the rule in this case is not accurate.