Question

The actual length of a desk is 58 1/2 inches. Margaret estimates the length of the desk and finds her percent error to be less than 5%.

What range of values represents Margaret's estimated length?

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Answer 1

Answer:

Margaret's estimated length is between 55.575 inches and 61.425 inches.

Step-by-step explanation:

I believe this is enough explanation

Answer 2

Percent error is error in percentage compared to original measurement. The range of values representing Margaret's estimated length is $M \in [ 55.575, \: \: 61.425] \: \rm (in \: inches)$

How to calculate the range of estimated measurement from percent error?

If the measurement of the object is measured to be M, and the percent error in the measurement is estimated to be E%, and O is the original measurement of the object being measured then:

$\rm M \in O \pm E\% \: \rm of \: \rm O$

where O is the original measurement of the object being measured.

This decides the range of values in which the original measurement can fall in. It is $\rm [ O - \text{E\% of O}, \: \: O + \text{E\% of O}]$

For the given case, we have:

Original measurement of the desk = O =  $58\dfrac{1}{2} = 58 + 0.5 = 58.5 \: \rm inches$

E% = percent error in measurement = 5%

Let M denotes the estimated measurement of the desk by Margaret.

Then, $M \in \rm [ 58.5 - \text{5\% of 58.5}, \: \: 58.5 + \text{5\% of 58.5}] \: \rm (in \: inches)$

5% of 58.5 is:

$\dfrac{58.5}{100} \times 5 = 2.925$ (inches).

Thus, the value of M will lie in:

$M \in \rm [ 58.5 - 2.925, \: \: 58.5 +2.925] \: \rm (in \: inches)\\\\M \in [ 55.575, \: \: 61.425] \: \rm (in \: inches)$

Thus, the range of values representing Margaret's estimated length is $M \in [ 55.575, \: \: 61.425] \: \rm (in \: inches)$

Learn more about percent error here:

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