A particular manufacturing design requires a shaft with a diameter between 22.87 mm and 23.012 mm. The manufacturing process yields shafts with diameters normally distributed, with a mean of 23.004 mm and a standard deviation of 0.004 mm. Complete parts (a) through (c). Click here to view page 1 of the cumulative standardized normal distribution table. Click here to view page 2 of the cumulative standardized normal distribution table. a. For this process what is the proportion of shafts with a diameter between 22.87 mm and 23.00 mm? The proportion of shafts with diameter between 22.87 mm and 23.00 mm is (Round to four decimal places as needed.)

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ISBN:9781119256830
Author:Amos Gilat
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**Educational Exercise: Statistical Normal Distribution in Manufacturing**

**Homework: Module 6, Part I**

**Problem 6.2.13**

- **Objective:** To determine the proportion of shafts produced with diameters falling within a specified range.

**Problem Statement:**
A manufacturing process designs shafts with diameters ranging from 22.87 mm to 23.012 mm. The diameters of the produced shafts are normally distributed, having:

- Mean (μ): 23.004 mm
- Standard deviation (σ): 0.004 mm

**Tasks:**

1. **Calculate the Proportion:**
   - Focus: Determine the proportion of shafts whose diameters lie between 22.87 mm and 23.00 mm.
   - Use the cumulative standardized normal distribution tables for calculations.
  
**Instructions:**

- Click the provided link to view how to use the cumulative standardized normal distribution table.
- Use the table to find the relevant probabilities and calculate the required proportion.

**Note:**
- The answer should be rounded to four decimal places.

**Graphical Components:**
- **Cumulative Standardized Normal Distribution Table:** Clickable links lead to visual data supporting the calculations.

**Submission:**
- Enter your calculated answer in the provided answer box.
- Click "Check Answer" to verify your response.

**Progress Tracker:** 
- Update on remaining problems: 2 parts left to be completed.

This exercise guides learners in applying statistical methods to practical manufacturing problems, utilizing normal distribution principles to assess production quality.
Transcribed Image Text:**Educational Exercise: Statistical Normal Distribution in Manufacturing** **Homework: Module 6, Part I** **Problem 6.2.13** - **Objective:** To determine the proportion of shafts produced with diameters falling within a specified range. **Problem Statement:** A manufacturing process designs shafts with diameters ranging from 22.87 mm to 23.012 mm. The diameters of the produced shafts are normally distributed, having: - Mean (μ): 23.004 mm - Standard deviation (σ): 0.004 mm **Tasks:** 1. **Calculate the Proportion:** - Focus: Determine the proportion of shafts whose diameters lie between 22.87 mm and 23.00 mm. - Use the cumulative standardized normal distribution tables for calculations. **Instructions:** - Click the provided link to view how to use the cumulative standardized normal distribution table. - Use the table to find the relevant probabilities and calculate the required proportion. **Note:** - The answer should be rounded to four decimal places. **Graphical Components:** - **Cumulative Standardized Normal Distribution Table:** Clickable links lead to visual data supporting the calculations. **Submission:** - Enter your calculated answer in the provided answer box. - Click "Check Answer" to verify your response. **Progress Tracker:** - Update on remaining problems: 2 parts left to be completed. This exercise guides learners in applying statistical methods to practical manufacturing problems, utilizing normal distribution principles to assess production quality.
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