Question

The ideal diameter of a rod needed for a machine is $75mm$.The actual diameter can vary from the ideal diameter by$0.05mm$.What range of diameters will be acceptable to the customer without causing the rod to be rejected ?

Short answer

The diameter of the rod can be between $74.95mm$ and $75.05mm$

Step-by-step solution

Given information

Ideal length = $75mm$

Tolerance =$0.05mm$

Calculation

Let x=the actual measurement

$$\begin{gathered} \left|actuallength-ideallength\right|\le tolerance \\ \left|x-75\right|\le 0.05 \\ -0.05\le x-75\le 0.05 \\ -0.05+75\le x\le 0.05+75 \\ 74.95\le x\le 75.05 \end{gathered}$$

The diameter of the rod can be between$74.95mm$and$75.05mm$