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Sagot :
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].
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].
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