Final answer:
Using the range rule of thumb by dividing the range of 586 cm by 4, the estimated standard deviation is approximately 146.5 cm, which must be a typo in the provided options. The exact standard deviation given is 178.9 cm.
Step-by-step explanation:
To use the range rule of thumb to estimate the standard deviation, we take the range of data and divide it by 4. The range is the difference between the highest and lowest value. In this case, the range is 1490 cm - 904 cm, which equals 586 cm.
When we divide 586 cm by 4, we get an estimated standard deviation of approximately 146.5 cm. However, among the given options, the closest estimate would be 146.5 cm / 2 (as the options seem to be misstated and do not align with the calculated standard deviation). We then compare this estimated value to the exact standard deviation of 178.9 cm.
It is important to note that while the range rule of thumb provides a quick estimate, it is not as accurate as the exact calculation of the standard deviation.