A puzzle company is interested in the average number of pieces in their jigsaw puzzles, so they plan to create a confidence interval for the true mean. The easiest puzzle in their line is $100$ pieces, and the largest is $1000$ pieces. Use the range rule of thumb to estimate the sample standard deviation.

• A. $275$
• B. $550$
• C. $450$
• D. $225$

Answer: (D)

Verified step by step guidance

1. Identify the minimum and maximum values of the data set. Here, the smallest puzzle has 100 pieces and the largest has 1000 pieces.
2. Calculate the range of the data using the formula: \(\text{Range} = \text{Maximum} - \text{Minimum}\).
3. Apply the range rule of thumb to estimate the sample standard deviation. The rule states: \(\text{Standard Deviation} \approx \frac{\text{Range}}{4}\).
4. Substitute the values into the formula: \(\text{Standard Deviation} \approx \frac{1000 - 100}{4}\).
5. Simplify the expression to find the estimated standard deviation, which will be used for further analysis such as constructing confidence intervals.