**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.

Let "X" be the diameter of shafts.

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.)

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.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

**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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