Question

The actual height of a book is 914 inches. Beverly estimates the height of the book and finds her percent error to be less than 4%.

What range of values represents Beverly's estimated height?

Enter your answers as decimals or mixed numbers in simplest form by filling in the boxes.

Beverly's estimated height is between
inches and
inches.

1 answer

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.

  1. 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: \[ \text{Estimated height} = \text{Actual height} \pm (\text{Actual height} \times \text{Percent error}) \]

  2. Calculate 4% of the actual height: \[ 0.04 \times 914 = 36.56 \text{ inches} \]

  3. 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.