Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 8 ounces.

**a. **The process standard deviation is 0.10, and the process control is set at plus or minus 2 standard deviations. Units with weights less than 7.8 or greater than 8.2 ounces will be classified as defects. What is the probability of a defect (to 4 decimals)?

In a production run of 1000 parts, how many defects would be found (to the nearest whole number)?

**b. **Through process design improvements, the process standard deviation can be reduced to 0.08. Assume the process control remains the same, with weights less than 7.8 or greater than 8.2 ounces being classified as defects. What is the probability of a defect (to 4 decimals)?

In a production run of 1000 parts, how many defects would be found (to the nearest whole number)?

**c. **What is the advantage of reducing process variation, thereby causing a problem limits to be at a greater number of standard deviations from the mean?

Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of ounces.

**a. **The process standard deviation is ounces, and the process control is set at plus or minus standard deviations. Units with weights less than or greater than ounces will be classified as defects. What is the probability of a defect (to 4 decimals)?

In a production run of parts, how many defects would be found (round to the nearest whole number)?

**b. **Through process design improvements, the process standard deviation can be reduced to ounces. Assume the process control remains the same, with weights less than or greater than ounces being classified as defects. What is the probability of a defect (round to 4 decimals; if necessary)?

In a production run of parts, how many defects would be found (to the nearest whole number)?

**c. **What is the advantage of reducing process variation, thereby causing a problem limits to be at a greater number of standard deviations from the mean?

Motorola used the **normal** **distribution** to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 10 ounces.

- The process standard deviation is 0.15 and the process control is set at plus or minus on standard deviation, so units with weights less than 9.85 oz or greater than 10.15 oz will be classified as defects. Find the probability of a defect
**and**the expected number of defects for a 1000-unit production run.

- Through process design improvements, suppose the process standard deviation can be reduced to 0.05. Assume the process control remains the same, so products with weights less than 9.85 and more than 10.15 ounces are classified as defects. Find the probability of a defect
**and**the expected number of defects for a 1000-unit production run.

- What is the advantage of reducing process variation (question 2)? In other words, explain (
**mathematically**) why reducing the standard deviation to 0.05 but keeping the process controls at 9.85 and 10.15 ounces led to better production outcomes.

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