**Problem 4: Shaft Manufacturing Specifications**Shafts manufactured for use in optical storage devices have diameters that are normally distributed with a mean (μ) of 0.659 cm and a standard deviation (σ) of 0.003 cm. The specification for the shaft diameter is 0.652 ± 0.006 cm.a) **What proportion of the shafts manufactured by this process meet the specifications?**b) **The process mean can be adjusted through calibration. If the mean is set to 0.651 cm, what proportion of the shafts will meet specifications?**c) **If the mean is set to 0.651 cm, what must the standard deviation be so that 92% of the shafts will meet specifications?****Explanation of Concepts:**In this problem, the goal is to determine how changes in the manufacturing process affect the proportion of shafts that meet given specifications. We explore how adjusting the mean or changing the standard deviation impacts compliance with quality standards.**Points of Analysis:**- The specification range is from 0.646 cm to 0.658 cm.- For part (a), calculate the z-scores to find the proportion that meets specifications.- For part (b), analyze the impact of changing the mean on specification compliance.- For part (c), determine the required standard deviation to meet a 92% compliance rate with a given mean.

Let X denotes the shaft diameter. Given that X~N(μ=0.659,σ2=(0.003)2). Let, Z=X-0.6590.003, then…

Answered: 4. Shafts manufactured for use in…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Q4: The diameter of a shaft in an optical storage drive is normally distributed with mean 0.2408 inch and standard deviation 0.0005 inch. The specifications on the shaft are 0.2400±0.001 inch. a) What proportion of shafts conforms to specifications? b) If the process is centered so that the process mean is equal to the target value of 0.2400, then what proportion of shafts conforms to specifications now?
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Q4: The diameter of a shaft in an optical storage drive is normally distributed with mean 0.2408 inch and standard deviation 0.0005 inch. The specifications on the shaft are 0.2400±0.001 inch. a) What proportion of shafts conforms to specifications? b) If the process is centered so that the process mean is equal to the target value of 0.2400, then what proportion of shafts conforms to specifications now?

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