Question

the race speeds (in minutes) for the top eight cars in a 200-mile race are listed below. use the range rule of thumb to estimate the standard deviation. round results to the nearest tenth. 181.0 180.6 189.2 182.2 175.6 180.0 177.9 181.8 a. 1.1 minutes b. 7.5 minutes c. 6.8 minutes d. 3.4 minutes

Explanation:

Step1: Find the range

First, identify the maximum and minimum values in the data set. The data points are: 181.0, 180.6, 189.2, 182.2, 175.6, 180.0, 177.9, 181.8.
The maximum value ($\text{Max}$) is 189.2, and the minimum value ($\text{Min}$) is 175.6.
The range is calculated as $\text{Range} = \text{Max} - \text{Min}$.
So, $\text{Range} = 189.2 - 175.6 = 13.6$.

Step2: Apply the range rule of thumb

The range rule of thumb states that the standard deviation ($s$) is approximately $\frac{\text{Range}}{4}$.
Substitute the range we found: $s \approx \frac{13.6}{4} = 3.4$. Wait, no—wait, did I miscalculate? Wait, no, wait the options: Wait, maybe I made a mistake. Wait, let's recheck the data. Wait, the data is race speeds (in minutes) for a 200 - mile race. Wait, the data points: 181.0, 180.6, 189.2, 182.2, 175.6, 180.0, 177.9, 181.8. Wait, maximum is 189.2, minimum is 175.6. Range is 189.2 - 175.6 = 13.6. Then range rule of thumb: standard deviation ≈ range / 4. So 13.6 / 4 = 3.4? But wait, the options include D. 3.4 minutes. Wait, but let me check again. Wait, maybe I misread the data. Wait, is 189.2 a typo? Wait, maybe it's 181.9? No, the user provided the data as is. So according to the range rule of thumb, standard deviation ≈ range / 4. So range is 189.2 - 175.6 = 13.6. 13.6 / 4 = 3.4. So the answer should be D.

Wait, but let me check the options again. The options are A. 1.1, B.7.5, C.6.8, D.3.4. So according to the calculation, it's 3.4.

Answer:

D. 3.4 minutes