Question

The ideal length of a particular metal rod is 35.5 cm. The measured length may vary from the ideal length by at most 0.035 cm. What is the range of acceptable lengths for the rod?

Answer 1

`35.465\leq x\leq 35.535`

Explanation:

Since it can vary by 0.035 cm, the "measured length" can be either 0.035 cm MORE THAN the ideal length or 0.035 cm LESS THAN the ideal length.

Lower bound, thus, can be 35.5 - 0.035 = 35.465 cm

Upper bound, thus, can be 35.5 + 0.035 = 35.535 cm

If we let measured length be x, then we can write the range as:

`35.465\leq x\leq 35.535` cm

Answer 2

Idea length (x) = 35.5 cm
Variance = 0.035 cm

Acceptable lengths: ideal length +/- variance = 35.5 +/-0.035 = 35.465 cm to 35.535 cm

The acceptable range of lengths: 35.465 ≤ x ≤ 35.535