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Let $-1.01< \mu< 16.17$ represent an interval on the number line. Complete parts (a) through (c) below.
(a) Find the value that is in the middle of the interval and let the variable $m$ represent that.
$m=\square$ (Type an integer or a decimal. Do not round:)
(b) Find the distance from the middle of the interval to either endpoint and let $E$ represent that.
$E=\square$ (Type an integer or a decimal. Do not round.)
(c) Write the given interval in the format $m \pm E$.
$\mathrm{m} \pm \mathrm{E}=\square \pm \square$ (Type integers or decimals. Do not round.)
Answer
So, the final answers are: (a) The middle of the interval is \(m = \boxed{7.58}\). (b) The distance from the middle of the interval to either endpoint is \(E = \boxed{8.59}\). (c) The interval can be written in the format \(m \pm E\) as \(\boxed{7.58 \pm 8.59}\).
Step 1 ：Let's denote the two endpoints of the interval as \(\mu_1 = -1.01\) and \(\mu_2 = 16.17\).
Step 2 ：To find the middle of the interval, we can average the two endpoints. This gives us \(m = \frac{\mu_1 + \mu_2}{2} = 7.58\).
Step 3 ：The distance from the middle of the interval to either endpoint is half the length of the interval. This can be calculated as \(E = \frac{\mu_2 - \mu_1}{2} = 8.59\).
Step 4 ：Finally, we can write the interval in the format \(m \pm E\) as \(7.58 \pm 8.59\).
Step 5 ：So, the final answers are: (a) The middle of the interval is \(m = \boxed{7.58}\). (b) The distance from the middle of the interval to either endpoint is \(E = \boxed{8.59}\). (c) The interval can be written in the format \(m \pm E\) as \(\boxed{7.58 \pm 8.59}\).
