Judging acceptability
Sometimes a quantity of parts have to be assessed to see if they are suitable or not.
Example
The weight of part of a train engine has to be in the range of \(560 \pm 2.3\,kg.\)
Five of these parts have already been made. They weigh:
| \(562.1kg\) | \(557.2kg\) | \(560.6kg\) | \(558.8kg\) | \(556.2kg\) |
| \(562.1kg\) |
| \(557.2kg\) |
| \(560.6kg\) |
| \(558.8kg\) |
| \(556.2kg\) |
Which of these parts are acceptable?
Answer
The largest acceptable weight is \(560 + 2.3 = 562.3\,kg.\)
The smallest acceptable weight is \(560 - 2.3 = 557.7\,kg.\)
The acceptable parts are those with weights \(562.1\,kg\), \(560.6\,kg\) and \(558.8\,kg\)
Now try the following questions.
Question
The length of part of a table lamp has to be in the range \(234 \pm 2\,mm\).
Seven of these parts have already been made. Their lengths are:
| \(235.1mm\) | \(233.5mm\) | \(236.7mm\) | \(231.9mm\) | \(232.2mm\) | \(235.7mm\) | \(231.5mm\) |
| \(235.1mm\) |
| \(233.5mm\) |
| \(236.7mm\) |
| \(231.9mm\) |
| \(232.2mm\) |
| \(235.7mm\) |
| \(231.5mm\) |
Which of these parts are acceptable?
The largest acceptable length is \(234 + 2 = 236\,mm\)
The smallest acceptable length is \(234 - 2 = 232\,mm\)
The acceptable parts are those with lengths \(235.1mm\), \(233.5mm\), \(232.2mm\) and \(235.7mm\).
Question
The length of part of a computer has to be in the range \(16.1 \pm 0.3\,mm.\)
Six of these parts have already been made. Their lengths are:
| \(16.5mm\) | \(16.9mm\) | \(15.9mm\) | \(16.1\) | \(16.2mm\) | \(15.7mm\) |
| \(16.5mm\) |
| \(16.9mm\) |
| \(15.9mm\) |
| \(16.1\) |
| \(16.2mm\) |
| \(15.7mm\) |
Which of these parts are acceptable?
The largest acceptable length is \(16.1 + 0.3 = 16.4\,mm\)
The smallest acceptable length is \(16.1 - 0.3 = 15.8\,mm\)
The acceptable parts are those with lengths:
\(15.9\,mm\), \(16.1\,mm\) and \(16.2\,mm\).