Sure, let's solve this problem step-by-step.
1. Determine the total number of units in the sample:
The total units in the sample is the sum of the units within tolerance and the units outside tolerance.
[tex]\[
\text{Total units} = 145 \ (\text{units within tolerance}) + 5 \ (\text{units outside tolerance}) = 150 \ \text{units}
\][/tex]
2. Calculate the percentage of units outside the tolerance:
To find the percentage of units outside the tolerance, divide the number of units outside tolerance by the total number of units in the sample and multiply by 100.
[tex]\[
\text{Percentage outside tolerance} = \left( \frac{\text{Units outside tolerance}}{\text{Total units}} \right) \times 100
\][/tex]
Substituting the given values:
[tex]\[
\text{Percentage outside tolerance} = \left( \frac{5}{150} \right) \times 100
\][/tex]
3. Perform the division and multiplication:
[tex]\[
\frac{5}{150} = 0.03333333333333333
\][/tex]
[tex]\[
0.03333333333333333 \times 100 = 3.3333333333333335 \%
\][/tex]
4. Round to the nearest percent:
The result is approximately 3.3333333333333335%, which rounds to the nearest whole number as:
[tex]\[
3 \%
\][/tex]
In conclusion, the percentage of the quality sample that is outside the tolerance is [tex]\(3 \%\)[/tex].
