To find the range of values that represents Beverly's estimated height, we start by calculating the acceptable error range based on the actual height of the book, which is 914 inches.
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Determine the maximum percent error: 4% of the actual height. \[ \text{Percent error} = \frac{\text{Estimated height} - \text{Actual height}}{\text{Actual height}} \times 100% \] We can express this in terms of actual height: \[ \text{Estimated height} = \text{Actual height} \pm (\text{Actual height} \times \text{Percent error}) \]
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Calculate 4% of the actual height: \[ 0.04 \times 914 = 36.56 \text{ inches} \]
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Calculate the range for estimated height: To find the lower and upper bounds:
- Lower bound: \( 914 - 36.56 = 877.44 \text{ inches} \)
- Upper bound: \( 914 + 36.56 = 950.56 \text{ inches} \)
Thus, Beverly's estimated height is between approximately \( 877.44 \) inches and \( 950.56 \) inches.
Final answer:
Beverly's estimated height is between 877.44 inches and 950.56 inches.