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 in the data set. Here, the smallest puzzle has 100 pieces and the largest has 1000 pieces.
2. Calculate the range by subtracting the minimum value from the maximum value: \(\text{Range} = 1000 - 100\).
3. Apply the range rule of thumb to estimate the sample standard deviation. The rule states that the standard deviation \(s\) can be approximated by dividing the range by 4: \(s \approx \frac{\text{Range}}{4}\).
4. Substitute the calculated range into the formula: \(s \approx \frac{1000 - 100}{4}\).
5. Simplify the expression to find the estimated sample standard deviation.