Question

A shaft with a diameter of 100 mm will be manufactured. The standard deviation of the shafts produced with the quality control was calculated as ± 0.1 mm. This shaft will rotate inside a bearing hole slightly larger than 100 mm in diameter. Accordingly, what should be the minimum hole diameter through which at least 90% of the manufactured shafts can pass.

          A shaft with a diameter of 100 mm will be manufactured. The standard deviation of the shafts produced with the quality control was calculated as ± 0.1 mm. This shaft will rotate inside a bearing hole slightly larger than 100 mm in diameter. Accordingly, what should be the minimum hole diameter through which at least 90% of the manufactured shafts can pass.
        
Show more…

Added by David D.

University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
A shaft with a diameter of 100 mm will be manufactured. The standard deviation of the shafts produced with the quality control was calculated as ± 0.1 mm. This shaft will rotate inside a bearing hole slightly larger than 100 mm in diameter. Accordingly, what should be the minimum hole diameter through which at least 90% of the manufactured shafts can pass.
Close icon
Play audio
Feedback
Powered by NumerAI
Kathleen Carty Jennifer Stoner
David Collins verified

Shannon K and 56 other subject Physics 101 Mechanics educators are ready to help you.

Ask a new question

*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

*

Key Concepts

-
Key Concept
Premium Feature
Explore the core concept behind this problem.
Play button
Key Concept
Premium Feature
Explore the core concept behind this problem.
Your browser does not support the video tag.

*

Recommended Videos

-
a-manufacturer-cuts-shafts-that-fit-into-a-valve-hole-the-design-calls-for-the-diameter-of-the-shafts-to-be-22000-mm-the-process-was-found-to-produce-shafts-with-a-mean-diameter-of-22002-and-48503

A manufacturer cuts shafts that fit into a valve hole. The design calls for the diameter of the shafts to be 22.000 mm. The process was found to produce shafts with a mean diameter of 22.002 and standard deviation of 0.005. What diameter will be exceeded by 2 percent of the shafts? Round to three decimals and include a leading zero if necessary. ((ANSWER IS NOT 22.012))

Shannon K.

a-shaft-and-hole-have-a-nominal-diameter-of-1-in-the-shaft-has-a-tolerance-of-0003in-the-hole-has-a-tolerance-of-0004in-and-the-allowance-is-set-at-0001in-the-dimensions-are-based-on-the-bas-91003

A shaft and hole have a nominal diameter of 1 in. The shaft has a tolerance of 0.003 in, the hole has a tolerance of 0.004 in, and the allowance is set at 0.001 in. The dimensions are based on the Basic Hole System. Show the deviations for the shaft and the hole from the nominal size; calculate the maximum and minimum clearance for two mating parts.

Adi S.

shaft-with-diameler-of-21000-mm-but-shafts-wilh-diameters-between-20992-mm-and-21008-mm-are-acceplable-the-a-particular-manufacturing-design-requires-with-diamelers-normally-distributed_-wit-14767

A particular manufacturing design requires a shaft with a diameter of 21.000 mm, but shafts with diameters between 20.992 mm and 21.008 mm are acceptable. The manufacturing process yields shafts with diameters normally distributed, with a mean of 21.003 mm and a standard deviation of 0.006 mm. Complete parts (a) through (d) below. a. For this process, what is the proportion of shafts with a diameter between 20.992 mm and 21.000 mm? The proportion of shafts with diameter between 20.992 mm and 21.000 mm is (Round to four decimal places as needed.)

Thuc N.


*

Recommended Textbooks

-
University Physics with Modern Physics

University Physics with Modern Physics

Hugh D. Young 14th Edition
achievement 1,956 solutions
Physics: Principles with Applications

Physics: Principles with Applications

Douglas C. Giancoli 7th Edition
achievement 1,219 solutions
Fundamentals of Physics

Fundamentals of Physics

David Halliday, Robert Resnick , Jearl Walker 10th Edition
achievement 1,924 solutions

*

Transcript

-
00:01 In this question we have given the diameter of the shaft is 22 .000 mm and the mean is given as 22 .002 mm and the standard deviation is given as 0 .005.
00:22 And we have to find that what diameter will exceed by 2 % of the shaft.
00:30 So we are given that x follows normal distribution with this mean and the standard deviation.
00:42 Now for top 2 % data let x be the required cutoff.
00:53 Now so we have probability when x is greater than x is equal to 2%.
01:00 So it implies probability when x is greater than x is equal to 0 .0 .02.
01:07 So it implies probability when x is less than x is equal to 1 minus probability when x is strictly greater than x.
01:17 This is equal to 1 minus 0 .02 and after subtracting it will get this 0 .9.
01:24 Now for the standard normal variable x...
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever