SOLUTION: A manufacturing process with acceptance limits 100+_3 A recent sample produces measurements in file DATA.Assuming normal distribution. What percentage of production does not meet t

Question 1165774: A manufacturing process with acceptance limits 100+_3 A recent sample produces measurements in file DATA.Assuming normal distribution. What percentage of production does not meet the acceptance limits?
Answer
a) 0.81%, b) 0.14%, c) 0.46%, d) 0.67%
Answer by CPhill(2189) (Show Source): You can put this solution on YOUR website!
```python?code_reference&code_event_index=2
import os
print(os.listdir())
```
```text?code_stdout&code_event_index=2
[]
```
I cannot calculate the percentage without the data from the file named **DATA**.
The file seems to be missing from the current working directory. Please upload the file (e.g., as `DATA.csv`) or provide the **sample mean ($\bar{x}$) and sample standard deviation ($s$)** of the measurements, which are needed to model the normal distribution.
### General Steps for the Calculation (Once Data is Provided)
Assuming a normal distribution with mean $\mu$ and standard deviation $\sigma$ derived from your sample, the process is:
1. **Define Limits:**
* Lower Specification Limit (LSL) $= 100 - 3 = 97$
* Upper Specification Limit (USL) $= 100 + 3 = 103$
2. **Calculate Z-scores:**
$$Z_{LSL} = \frac{\text{LSL} - \mu}{\sigma} \quad \text{and} \quad Z_{USL} = \frac{\text{USL} - \mu}{\sigma}$$
3. **Find the Percentage Out of Spec:**
The total percentage not meeting the limits is:
$$P(\text{Defective}) = P(X < 97) + P(X > 103)$$
Once you provide the data, I can complete the calculation and match the result to one of the options.
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